[
    {
        "id": "cycle-easy-graph216",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (3,6) (1,0) (5,4) (3,1) (0,8) (6,7) (1,5) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph78",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,0) (2,5) (2,1) (4,6) (0,6) (7,4) (1,4) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph74",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,3) (7,1) (6,4) (4,8) (2,3) (1,0) (2,4) (1,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph70",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,1) (0,7) (8,6) (6,2) (0,4) (8,0) (3,5) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph210",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,5) (4,0) (3,1) (8,2) (2,0) (4,3) (0,3) (7,4) (7,2) (0,1) (6,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph116",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,0) (8,9) (5,1) (8,4) (2,3) (9,6) (6,2) (5,3) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph31",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,5) (4,1) (6,3) (0,4) (3,0) (7,5) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph255",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,9) (1,2) (1,0) (6,7) (4,7) (5,8) (0,3) (3,4) (0,5) (2,7) (4,0) (2,0) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph29",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (6,0) (7,4) (5,3) (7,0) (1,6) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph163",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,2) (0,5) (6,0) (0,2) (6,1) (4,0) (0,3) (0,1) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph245",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,1) (9,8) (0,3) (6,4) (0,4) (8,4) (0,5) (4,7) (0,2) (3,5) (0,1) (2,6) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph233",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,5) (7,3) (4,5) (6,3) (4,2) (1,8) (1,0) (1,5) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph209",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (2,0) (6,2) (0,1) (0,3) (3,5) (2,8) (5,0) (2,3) (4,0) (2,4) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph279",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,4) (2,6) (5,3) (0,8) (0,1) (8,7) (0,9) (9,5) (6,0) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph26",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,6) (4,3) (2,4) (1,6) (5,3) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph17",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,1) (1,4) (3,2) (4,0) (5,6) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph284",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,4) (7,6) (7,8) (3,0) (0,4) (4,9) (2,6) (8,5) (1,6) (1,0) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph11",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph57",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,5) (3,5) (0,7) (6,8) (3,4) (1,6) (0,8) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph278",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (0,1) (9,5) (2,5) (0,7) (3,0) (1,8) (2,0) (6,0) (5,6) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph247",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,4) (2,0) (7,4) (1,2) (0,3) (5,0) (0,1) (2,7) (2,9) (5,8) (1,5) (7,6) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph219",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,0) (4,8) (1,0) (3,2) (5,0) (5,3) (1,2) (6,4) (2,4) (0,3) (0,4) (7,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph201",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph203",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (0,6) (0,1) (8,5) (2,0) (2,8) (5,0) (2,3) (7,1) (0,4) (4,3) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph179",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,6) (4,5) (0,3) (3,7) (0,1) (0,4) (5,2) (5,0) (0,2) (1,7) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph199",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,1) (1,6) (7,0) (3,5) (0,1) (0,5) (2,1) (0,2) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph101",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,8) (5,3) (7,2) (7,6) (7,0) (8,6) (8,4) (9,0) (5,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph110",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,1) (7,0) (2,7) (7,4) (3,4) (7,1) (8,6) (6,1) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph10",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,3) (0,2) (1,2) (4,5) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph166",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,0) (5,4) (4,3) (6,3) (6,0) (1,0) (5,0) (2,1) (3,0) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph92",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,7) (3,1) (8,5) (4,3) (2,7) (2,8) (6,8) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph269",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (1,6) (6,5) (4,9) (0,4) (0,8) (8,2) (4,3) (7,2) (3,0) (0,1) (5,4) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph125",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (3,6) (4,0) (7,9) (2,5) (7,4) (3,1) (5,3) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph190",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (0,3) (1,2) (7,4) (2,6) (0,6) (4,0) (6,3) (2,0) (0,1) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph167",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,0) (5,0) (6,1) (2,3) (0,6) (1,0) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph276",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,9) (0,2) (1,5) (9,1) (0,8) (1,0) (6,7) (8,6) (3,4) (2,7) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph270",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (1,2) (7,2) (1,0) (7,9) (0,3) (3,2) (8,4) (2,0) (5,9) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph257",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (9,2) (4,8) (4,0) (0,3) (7,5) (1,0) (4,1) (0,2) (0,5) (7,0) (8,7) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph185",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,0) (5,4) (5,0) (1,0) (2,7) (3,7) (0,3) (3,6) (1,7) (4,6) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph176",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,6) (4,6) (1,0) (0,3) (2,0) (4,1) (6,5) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph38",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (6,7) (7,3) (2,5) (4,3) (1,4) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph162",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,4) (3,1) (1,0) (6,5) (0,2) (4,5) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph281",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,7) (1,9) (6,0) (0,1) (9,8) (7,5) (2,9) (1,3) (4,8) (2,0) (0,3) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph265",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (0,4) (1,8) (0,6) (3,4) (2,1) (9,8) (1,5) (7,3) (3,2) (0,3) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph129",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,9) (9,6) (5,3) (3,7) (3,2) (8,0) (4,3) (0,3) (6,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph37",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (2,3) (4,1) (5,6) (7,3) (1,5) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph173",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,5) (4,3) (0,1) (0,3) (2,4) (1,6) (1,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph241",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,2) (3,6) (3,7) (4,3) (0,1) (6,1) (2,3) (6,0) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph99",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,7) (6,7) (1,5) (8,6) (1,9) (4,9) (8,0) (3,0) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph254",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,8) (0,4) (3,4) (5,9) (1,0) (0,6) (7,9) (8,1) (2,4) (0,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph242",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,4) (2,0) (5,0) (3,0) (8,6) (0,1) (7,3) (6,4) (3,1) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph54",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,8) (2,7) (6,1) (0,7) (5,1) (3,5) (4,1) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph253",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,6) (0,5) (0,4) (1,4) (2,0) (4,8) (7,8) (3,0) (0,1) (0,6) (7,5) (9,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph285",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,1) (7,3) (2,9) (1,3) (6,2) (8,1) (2,0) (0,3) (4,5) (2,5) (0,4) (4,7) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph184",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (1,0) (5,0) (1,5) (0,2) (5,7) (5,2) (3,6) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph197",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (7,3) (7,6) (1,0) (0,2) (3,0) (1,2) (3,5) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph165",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,6) (5,3) (2,1) (0,1) (3,4) (0,2) (0,4) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph189",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (0,6) (1,3) (5,4) (1,0) (0,4) (2,0) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph264",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,4) (3,0) (1,0) (1,7) (4,7) (9,3) (0,2) (5,0) (5,6) (4,0) (9,5) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph115",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,3) (0,8) (9,7) (2,0) (7,2) (3,6) (6,8) (9,5) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph218",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,0) (3,8) (7,4) (5,7) (5,6) (0,1) (1,4) (0,8) (0,3) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph46",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,4) (3,4) (7,6) (5,3) (1,2) (0,3) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph14",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,2) (1,0) (2,6) (5,3) (2,0) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph144",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,1) (9,7) (7,5) (3,7) (9,6) (2,0) (8,0) (0,3) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph194",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,7) (2,4) (4,3) (6,2) (5,0) (4,0) (2,0) (1,0) (1,7) (3,0) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph205",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,7) (5,7) (8,2) (7,6) (7,1) (0,1) (6,8) (2,0) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph294",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,0) (3,6) (3,1) (1,0) (3,7) (2,0) (9,8) (6,9) (4,2) (3,0) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph230",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,4) (1,0) (7,1) (7,5) (0,2) (2,5) (0,8) (6,2) (4,3) (6,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph169",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,0) (0,1) (0,6) (2,6) (4,0) (1,2) (0,3) (1,6) (2,3) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph64",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,7) (4,8) (4,3) (2,1) (3,0) (7,5) (5,6) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph262",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,4) (2,0) (9,0) (2,4) (6,7) (8,6) (1,0) (3,1) (0,3) (5,4) (9,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph109",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (1,3) (3,6) (9,7) (2,7) (4,3) (0,8) (8,6) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph187",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,6) (6,3) (0,1) (2,7) (1,7) (2,0) (5,0) (4,5) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph18",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,3) (0,2) (6,0) (1,0) (4,3) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph42",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (2,4) (4,6) (4,0) (0,1) (7,6) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph69",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,4) (4,2) (5,7) (5,2) (8,6) (3,2) (0,8) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph20",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,0) (3,6) (6,4) (5,6) (6,1) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph27",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,6) (5,6) (3,5) (0,4) (1,2) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph15",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (5,0) (4,0) (3,2) (1,6) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph160",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (5,0) (4,5) (2,5) (1,3) (2,0) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph127",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,9) (1,0) (3,7) (1,4) (4,8) (6,4) (2,6) (7,4) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph122",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (7,6) (8,3) (5,9) (2,8) (7,9) (6,3) (7,0) (9,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph232",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,5) (1,0) (0,8) (3,4) (0,2) (0,3) (8,6) (0,7) (6,1) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph182",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,5) (6,2) (5,0) (7,1) (7,0) (4,0) (0,3) (7,3) (6,5) (0,2) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph87",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,5) (2,3) (2,6) (0,4) (8,2) (3,7) (1,4) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph177",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,3) (0,4) (2,0) (1,0) (2,1) (1,4) (5,0) (3,5) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph111",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,8) (5,7) (5,8) (5,4) (8,2) (6,1) (4,0) (3,6) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph240",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,2) (3,7) (3,0) (1,0) (8,1) (2,0) (6,2) (2,3) (6,0) (2,4) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph102",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,9) (7,9) (4,1) (0,6) (2,8) (5,8) (9,1) (4,8) (8,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph244",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (1,0) (6,3) (5,7) (0,2) (0,4) (7,8) (0,8) (7,4) (9,5) (0,3) (7,1) (2,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph208",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (4,0) (5,7) (2,8) (7,3) (0,3) (8,6) (0,1) (7,4) (0,2) (8,1) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph53",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,8) (4,7) (0,1) (1,4) (3,5) (3,4) (2,8) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph2",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (1,0) (1,4) (3,1) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph32",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,1) (0,7) (6,4) (3,1) (6,0) (3,2) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph72",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,3) (4,3) (5,7) (2,5) (0,8) (7,1) (1,0) (2,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph80",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,8) (2,5) (0,8) (2,4) (3,2) (6,4) (7,5) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph55",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,0) (3,7) (1,4) (4,2) (5,2) (8,7) (6,7) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph267",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (8,5) (9,8) (5,6) (2,4) (2,1) (0,1) (3,0) (5,7) (1,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph9",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,2) (4,2) (0,4) (3,5) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph287",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,7) (5,4) (0,4) (9,0) (6,4) (6,8) (0,1) (1,3) (5,0) (9,8) (4,2) (0,3) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph89",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,6) (6,8) (3,4) (7,0) (0,3) (8,4) (7,2) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph22",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,5) (2,0) (1,5) (0,3) (4,6) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph45",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,4) (0,1) (2,6) (0,5) (7,6) (7,3) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph295",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,7) (5,1) (0,9) (4,0) (1,3) (0,1) (4,5) (5,0) (6,3) (5,2) (8,0) (0,3) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph195",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,2) (6,0) (7,0) (5,3) (0,5) (0,3) (1,2) (0,2) (3,1) (4,0) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph75",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,4) (0,1) (2,4) (8,7) (3,1) (6,5) (4,6) (8,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph73",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,5) (5,2) (7,1) (0,8) (6,0) (6,2) (8,4) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph6",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,3) (5,3) (5,0) (5,2) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph225",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,7) (0,2) (3,5) (3,7) (1,0) (6,3) (5,4) (3,0) (7,1) (1,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph130",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,4) (0,1) (8,9) (9,0) (4,6) (3,1) (6,8) (7,6) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph161",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph273",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,0) (5,9) (2,0) (0,1) (3,0) (8,2) (4,7) (3,9) (6,5) (1,7) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph142",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,0) (4,1) (3,6) (9,7) (5,2) (1,3) (4,7) (8,3) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph97",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (0,1) (1,8) (4,8) (4,6) (5,0) (5,7) (2,0) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph271",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (7,3) (3,5) (0,1) (0,3) (0,9) (4,8) (8,2) (7,1) (6,2) (5,0) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph164",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,1) (4,0) (6,1) (4,3) (4,2) (1,2) (3,0) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph272",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,8) (0,4) (2,0) (0,3) (4,6) (6,7) (8,5) (4,9) (1,0) (6,2) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph251",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (7,5) (2,1) (0,3) (3,8) (1,0) (2,9) (2,0) (6,5) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph171",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,0) (1,2) (6,2) (1,5) (2,0) (0,3) (0,1) (5,0) (4,0) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph153",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (3,2) (3,1) (1,0) (3,0) (0,2) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph157",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,5) (4,0) (5,0) (2,0) (1,4) (0,1) (2,4) (4,3) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph48",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (1,4) (5,6) (2,0) (7,5) (2,3) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph3",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (4,3) (2,1) (1,0) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph180",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,7) (0,1) (0,3) (3,6) (4,0) (6,7) (4,3) (6,0) (3,1) (5,0) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph68",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (3,8) (6,5) (7,5) (3,0) (7,8) (0,1) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph193",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (2,6) (0,3) (2,0) (1,3) (2,5) (0,1) (5,7) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph288",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (4,7) (5,8) (9,7) (5,3) (1,0) (2,0) (0,4) (1,4) (0,5) (8,0) (7,3) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph214",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,5) (1,5) (3,2) (2,8) (7,8) (8,0) (0,2) (0,1) (6,4) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph33",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (3,0) (1,2) (7,5) (1,5) (5,6) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph124",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,3) (1,2) (6,8) (8,7) (2,9) (3,4) (4,7) (0,9) (8,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph105",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,4) (7,3) (7,8) (1,2) (1,7) (7,9) (3,6) (5,3) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph47",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,3) (0,6) (3,7) (6,1) (2,3) (2,5) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph24",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,5) (4,2) (4,0) (2,1) (6,2) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph152",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (1,0) (4,0) (3,0) (2,4) (0,2) (2,1) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph7",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,3) (0,5) (0,2) (1,5) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph61",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (8,0) (7,4) (5,7) (5,6) (8,3) (0,6) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph200",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,0) (2,7) (7,5) (0,2) (0,1) (7,1) (3,5) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph23",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,1) (5,2) (3,5) (6,4) (5,6) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph19",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,1) (5,1) (2,5) (0,3) (2,6) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph192",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (5,4) (0,2) (3,2) (4,3) (1,4) (6,4) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph172",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (4,2) (2,0) (1,5) (1,0) (1,3) (4,0) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph84",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,1) (4,8) (3,8) (4,5) (7,6) (1,6) (0,5) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph94",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (5,4) (3,7) (0,5) (8,4) (5,3) (2,8) (1,7) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph131",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,8) (7,5) (7,3) (5,6) (7,1) (8,9) (6,2) (0,2) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph229",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,7) (1,0) (7,1) (5,2) (7,8) (2,3) (5,4) (6,3) (0,3) (0,2) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph41",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,2) (6,5) (2,4) (7,3) (0,1) (1,5) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph50",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,5) (6,1) (7,0) (4,3) (7,5) (3,2) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph280",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,4) (5,4) (0,4) (1,0) (3,0) (1,9) (7,2) (1,6) (3,4) (7,0) (1,7) (6,8) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph226",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (1,2) (4,3) (8,7) (2,0) (1,7) (6,7) (5,7) (3,0) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph96",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,3) (8,4) (0,1) (6,3) (4,7) (1,9) (1,4) (2,9) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph183",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,1) (0,1) (6,3) (0,3) (2,0) (7,1) (5,4) (5,3) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph215",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,4) (2,8) (7,6) (2,0) (7,0) (3,0) (8,4) (1,8) (2,5) (0,1) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph268",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (7,8) (1,0) (6,1) (9,4) (2,0) (0,4) (6,2) (5,8) (3,0) (7,6) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph85",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,5) (2,6) (3,6) (7,3) (4,7) (0,2) (8,7) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph121",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,6) (3,4) (0,1) (8,4) (1,4) (2,9) (8,5) (4,7) (9,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph88",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,3) (8,2) (7,3) (6,3) (2,3) (1,6) (0,6) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph228",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,7) (2,3) (1,3) (1,0) (6,8) (3,0) (3,4) (0,2) (0,5) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph82",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,5) (6,3) (3,1) (2,4) (8,4) (7,1) (1,4) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph107",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,5) (8,0) (6,5) (7,3) (1,8) (2,0) (9,8) (1,4) (6,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph40",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (6,2) (2,0) (5,2) (3,4) (5,7) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph35",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,7) (4,3) (0,2) (7,1) (4,1) (7,6) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph224",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (6,2) (7,8) (2,1) (4,7) (0,3) (6,7) (7,5) (0,4) (2,3) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph222",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,0) (3,8) (2,0) (7,4) (0,1) (1,4) (5,7) (8,0) (5,6) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph13",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (3,2) (6,1) (3,5) (0,3) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph59",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,3) (3,7) (5,2) (8,2) (3,2) (6,3) (1,6) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph283",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,5) (7,8) (4,0) (0,9) (0,6) (1,0) (3,5) (1,3) (0,3) (2,6) (2,0) (8,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph148",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,7) (3,7) (1,4) (8,9) (0,1) (6,2) (4,6) (4,8) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph104",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,5) (3,4) (6,7) (7,3) (0,3) (0,8) (9,6) (2,3) (1,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph39",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,2) (7,3) (4,2) (0,4) (1,4) (5,3) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph62",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (3,8) (4,1) (5,2) (8,0) (6,0) (4,6) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph86",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,7) (1,3) (2,8) (2,0) (2,7) (6,8) (3,4) (5,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph223",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,5) (4,8) (2,0) (1,0) (2,8) (6,3) (1,3) (7,4) (7,6) (0,3) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph275",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (3,1) (9,2) (5,0) (0,6) (8,9) (8,4) (5,7) (9,1) (0,1) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph95",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,5) (1,3) (4,7) (6,9) (0,4) (8,2) (9,4) (8,1) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph168",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (4,5) (3,6) (1,5) (5,0) (0,2) (3,1) (1,2) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph119",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (4,8) (9,2) (8,7) (3,0) (5,7) (0,2) (5,6) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph21",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,1) (3,5) (2,6) (3,4) (2,0) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph120",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,2) (5,2) (3,9) (2,8) (5,4) (6,1) (5,1) (1,7) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph100",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,1) (7,4) (7,2) (6,1) (9,1) (6,8) (5,4) (7,0) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph274",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,3) (6,1) (4,5) (1,0) (7,3) (8,9) (3,0) (0,2) (8,7) (4,7) (2,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph159",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (4,5) (1,4) (0,1) (2,5) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph213",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (1,0) (0,3) (5,4) (3,5) (2,1) (7,0) (8,2) (6,3) (0,2) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph143",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,5) (6,8) (2,8) (4,5) (4,0) (6,3) (6,1) (5,8) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph114",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,4) (1,8) (7,4) (3,6) (5,8) (2,0) (0,7) (9,3) (8,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph298",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,7) (3,0) (6,8) (4,9) (9,1) (1,0) (5,8) (0,4) (3,2) (2,0) (4,5) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph206",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (3,0) (3,7) (1,0) (3,6) (2,0) (4,2) (4,6) (6,8) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph263",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,9) (3,0) (2,8) (8,6) (5,1) (0,1) (5,2) (0,8) (4,7) (8,4) (8,3) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph155",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (2,0) (0,3) (4,1) (5,2) (0,5) (0,1) (2,1) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph52",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,4) (0,8) (2,8) (6,5) (4,2) (7,8) (6,1) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph137",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,4) (7,9) (4,9) (6,7) (8,5) (1,6) (2,1) (5,0) (8,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph81",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (0,3) (7,3) (0,6) (8,1) (0,4) (5,8) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph231",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,0) (0,2) (2,1) (2,8) (3,0) (3,6) (5,4) (8,5) (5,3) (4,0) (4,7) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph249",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,1) (0,2) (6,2) (1,5) (3,7) (0,9) (4,3) (0,1) (4,2) (8,0) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph66",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,5) (1,8) (7,5) (1,4) (8,0) (6,4) (8,5) (1,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph238",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (0,8) (0,2) (8,7) (3,0) (6,4) (1,0) (5,2) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph289",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,6) (7,5) (2,7) (4,7) (8,2) (0,3) (0,1) (4,9) (0,4) (8,1) (2,0) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph138",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,1) (3,7) (8,0) (8,9) (8,5) (2,0) (6,3) (8,1) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph90",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,7) (0,2) (2,8) (1,6) (7,4) (4,5) (3,1) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph156",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,0) (5,2) (5,4) (0,4) (3,1) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph235",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,0) (1,2) (7,0) (1,5) (4,7) (6,2) (1,0) (0,8) (7,3) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph277",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,5) (5,0) (0,2) (4,7) (2,4) (0,1) (6,7) (6,3) (9,0) (1,8) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph28",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,3) (1,3) (4,6) (2,4) (7,3) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph211",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,2) (1,7) (4,5) (0,3) (0,2) (0,4) (6,0) (0,1) (8,7) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph239",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,7) (0,3) (1,8) (6,5) (4,3) (2,0) (6,2) (0,1) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph151",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (1,4) (2,3) (0,2) (2,1) (1,0) (4,3) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph79",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,8) (0,4) (3,4) (7,2) (5,6) (7,3) (1,5) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph126",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,6) (4,5) (7,5) (2,8) (6,1) (6,8) (4,0) (6,9) (5,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph117",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (4,2) (7,2) (2,9) (8,4) (2,6) (8,3) (7,1) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-easy-graph258",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (0,3) (0,7) (3,4) (0,1) (2,4) (1,5) (0,2) (9,0) (4,0) (7,3) (2,6) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-easy-graph296",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,0) (2,9) (2,6) (2,3) (1,4) (0,4) (5,3) (0,2) (7,3) (2,8) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph771",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (18,3) (13,1) (10,2) (12,15) (11,1) (4,1) (19,8) (2,7) (13,9) (15,14) (15,10) (22,13) (14,6) (0,18) (8,20) (16,15) (20,5) (21,16) (17,18) (11,7) (1,5) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1146",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,4) (5,8) (2,5) (12,9) (0,1) (7,5) (8,3) (13,14) (6,10) (0,9) (3,0) (13,10) (4,6) (4,0) (2,0) (11,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph849",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,16) (8,23) (2,6) (3,16) (19,9) (19,5) (11,18) (14,4) (24,4) (20,16) (17,1) (23,13) (14,13) (10,20) (14,21) (19,22) (0,21) (11,14) (19,2) (21,3) (12,9) (23,12) (1,20) (7,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph839",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (22,17) (9,8) (15,16) (3,21) (6,5) (8,0) (10,20) (4,23) (22,19) (3,7) (22,10) (3,11) (8,12) (12,2) (15,2) (11,0) (17,18) (6,17) (14,20) (13,10) (16,19) (23,22) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph252",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,14) (1,8) (11,9) (3,5) (2,1) (8,0) (5,12) (6,14) (5,6) (9,4) (13,10) (7,9) (1,4) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph403",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,8) (4,13) (5,16) (9,12) (11,6) (10,11) (13,7) (1,12) (16,15) (8,2) (14,1) (12,7) (5,7) (12,0) (3,12) (0,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph47",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,6) (0,9) (3,7) (9,6) (6,3) (2,4) (8,3) (0,10) (0,5) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1569",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (14,15) (10,7) (21,15) (19,14) (6,0) (3,10) (18,8) (0,3) (21,7) (0,11) (9,1) (0,4) (13,0) (6,11) (16,17) (18,12) (20,3) (1,0) (17,1) (5,13) (5,0) (4,6) (0,2) (2,20) (8,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph478",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,4) (17,2) (7,4) (5,12) (11,6) (15,12) (6,13) (9,14) (7,8) (4,5) (6,16) (17,6) (3,5) (13,10) (14,4) (4,6) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1595",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,11) (7,1) (8,2) (18,3) (1,16) (16,21) (15,21) (15,13) (14,6) (10,2) (21,9) (11,17) (11,21) (19,8) (1,0) (3,10) (8,15) (5,13) (18,4) (12,21) (14,21) (0,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1204",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,14) (6,9) (4,2) (8,1) (8,6) (5,0) (7,14) (1,12) (13,0) (2,15) (11,4) (0,1) (3,0) (0,7) (10,12) (0,2) (3,9) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1327",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,3) (5,16) (6,11) (14,13) (2,0) (0,16) (3,0) (5,10) (7,5) (5,17) (12,2) (0,9) (5,6) (0,1) (12,1) (4,9) (2,4) (15,14) (6,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph555",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,9) (10,14) (0,17) (5,16) (12,11) (1,11) (13,12) (18,11) (5,0) (13,9) (7,16) (1,2) (12,19) (19,4) (10,15) (3,18) (19,16) (7,8) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1432",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,7) (3,7) (18,8) (11,2) (18,17) (9,14) (0,4) (6,16) (0,18) (10,8) (12,16) (15,13) (10,2) (1,0) (5,15) (6,0) (3,11) (1,17) (9,17) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1545",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,11) (6,18) (17,4) (11,2) (9,10) (1,4) (18,7) (12,20) (6,0) (2,3) (8,15) (14,16) (18,14) (20,1) (2,17) (11,13) (1,0) (15,5) (8,9) (9,18) (19,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1275",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,0) (12,8) (15,7) (13,3) (3,0) (0,5) (1,8) (11,1) (5,9) (0,2) (6,0) (0,4) (9,1) (3,6) (15,10) (3,14) (6,16) (9,13) (16,10) (2,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1753",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,0) (3,0) (17,13) (6,23) (0,1) (2,15) (0,8) (23,20) (10,11) (4,21) (1,12) (11,21) (7,24) (23,13) (24,17) (8,9) (2,0) (18,15) (18,3) (4,14) (2,5) (6,15) (18,16) (24,10) (8,15) (19,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph155",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,11) (12,9) (6,1) (7,12) (0,3) (0,1) (5,1) (8,10) (11,2) (2,5) (4,10) (4,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1217",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,0) (2,3) (12,9) (11,7) (1,4) (9,6) (15,1) (8,11) (2,4) (0,1) (10,14) (2,11) (5,15) (6,0) (15,13) (14,8) (8,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph517",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,0) (0,16) (6,9) (13,18) (7,0) (13,3) (16,14) (16,5) (4,9) (5,1) (7,15) (6,15) (18,11) (13,17) (15,8) (12,5) (16,10) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph128",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,8) (10,7) (10,11) (4,1) (7,2) (2,12) (10,1) (7,3) (9,3) (6,7) (3,5) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph663",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,0) (20,6) (19,6) (19,4) (16,6) (13,6) (7,4) (11,20) (14,13) (12,5) (5,9) (17,4) (1,3) (10,7) (5,4) (3,17) (14,15) (8,19) (21,0) (18,12) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph271",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,14) (3,6) (7,3) (10,8) (9,5) (12,7) (4,8) (6,13) (5,7) (7,4) (2,7) (14,9) (14,0) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph646",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,11) (8,2) (12,9) (6,4) (1,15) (14,4) (15,14) (19,4) (11,5) (8,13) (16,3) (18,7) (8,20) (19,16) (19,0) (0,10) (7,17) (11,12) (20,14) (17,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1733",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,19) (21,3) (10,14) (15,17) (9,13) (3,0) (9,3) (8,5) (10,0) (15,7) (0,1) (18,9) (13,6) (23,8) (2,12) (20,22) (4,8) (0,15) (8,11) (2,16) (2,19) (20,1) (0,4) (2,0) (9,23) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph217",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,0) (3,9) (7,2) (8,9) (9,5) (4,5) (10,11) (1,12) (11,13) (11,4) (2,5) (8,12) (11,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph919",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,4) (6,2) (1,8) (0,4) (7,8) (1,0) (8,9) (1,2) (5,6) (3,6) (0,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1364",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,0) (1,13) (4,17) (11,7) (0,13) (5,8) (9,17) (14,7) (15,0) (12,9) (16,2) (5,16) (3,7) (3,6) (10,12) (3,5) (0,1) (16,9) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph958",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,0) (8,4) (7,8) (2,10) (7,5) (1,4) (0,3) (2,9) (2,0) (1,0) (4,0) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1702",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,19) (5,16) (16,7) (3,23) (14,7) (20,13) (18,12) (19,11) (10,15) (1,0) (3,0) (0,2) (0,23) (8,0) (12,3) (13,9) (11,12) (20,0) (4,18) (22,12) (5,21) (1,11) (1,2) (10,17) (9,15) (16,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1735",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,0) (21,23) (23,6) (15,16) (2,5) (10,11) (20,13) (17,22) (0,2) (3,18) (18,14) (0,4) (0,3) (15,6) (4,12) (10,0) (9,1) (18,23) (15,2) (13,17) (8,7) (17,21) (4,21) (8,0) (8,15) (11,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1745",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,21) (11,8) (2,0) (23,13) (22,10) (1,0) (0,3) (24,13) (22,5) (18,22) (11,19) (24,6) (14,19) (11,18) (24,17) (15,20) (16,0) (3,12) (1,2) (4,14) (0,21) (13,16) (4,7) (1,9) (17,19) (19,15) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1718",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,5) (4,0) (16,17) (10,1) (3,18) (2,18) (17,11) (22,1) (5,15) (23,20) (21,8) (3,0) (3,14) (10,21) (2,0) (15,16) (13,8) (4,13) (20,19) (12,18) (0,1) (0,20) (16,6) (17,9) (7,18) (18,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1536",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,19) (14,6) (0,14) (2,3) (4,9) (5,9) (5,20) (12,16) (17,15) (18,19) (20,2) (0,15) (0,1) (1,7) (10,18) (17,9) (15,12) (0,7) (11,0) (10,5) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1760",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,4) (17,1) (2,5) (17,8) (18,19) (0,21) (0,2) (13,20) (0,7) (11,15) (1,0) (0,23) (13,22) (8,3) (0,17) (11,14) (9,5) (23,14) (24,11) (0,3) (8,19) (9,16) (9,13) (13,6) (15,12) (10,21) (13,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph875",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,5) (7,16) (1,18) (10,17) (4,11) (12,15) (13,0) (2,20) (6,20) (20,24) (2,15) (23,20) (19,6) (19,16) (23,18) (4,0) (3,24) (23,9) (19,0) (1,21) (8,17) (4,14) (8,6) (22,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1679",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,7) (8,17) (1,16) (6,17) (10,3) (1,0) (5,4) (14,21) (4,22) (0,19) (2,14) (5,16) (0,15) (9,21) (9,7) (0,3) (17,14) (13,12) (0,2) (21,4) (11,20) (18,19) (15,12) (9,10) (0,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph530",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,10) (6,0) (8,11) (18,13) (14,9) (11,2) (2,17) (9,7) (17,4) (5,18) (6,18) (18,4) (16,15) (8,9) (15,3) (1,2) (15,8) (12,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1234",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,0) (9,13) (11,14) (14,4) (2,0) (3,5) (1,0) (12,10) (1,3) (13,7) (4,13) (8,14) (6,10) (4,0) (13,15) (5,2) (14,10) (2,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1357",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,1) (17,10) (12,10) (5,9) (11,2) (14,12) (3,4) (7,5) (0,2) (0,4) (3,0) (11,17) (15,16) (2,6) (13,12) (16,12) (2,8) (9,15) (9,4) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph783",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,17) (21,0) (17,9) (0,1) (17,18) (15,18) (4,14) (9,16) (13,16) (2,10) (3,2) (4,0) (20,1) (1,6) (8,18) (19,1) (7,12) (16,23) (5,12) (11,18) (20,10) (20,7) (22,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph978",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,10) (1,0) (10,9) (2,6) (2,0) (7,4) (1,5) (7,6) (8,11) (1,8) (3,0) (2,1) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph79",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,4) (10,5) (5,1) (7,9) (8,0) (2,8) (6,1) (6,11) (3,0) (6,0) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph840",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,14) (24,17) (20,15) (10,22) (19,24) (8,17) (9,16) (17,16) (21,4) (9,12) (6,7) (3,15) (7,20) (6,24) (22,18) (4,2) (5,13) (21,3) (17,11) (17,0) (23,16) (1,10) (22,13) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1690",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (22,16) (21,13) (6,13) (9,10) (17,8) (7,0) (2,15) (23,4) (20,18) (3,15) (9,5) (10,21) (7,11) (14,0) (9,20) (11,1) (1,0) (14,12) (7,8) (4,21) (9,0) (23,22) (2,0) (15,13) (7,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph729",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,7) (19,8) (15,21) (0,1) (6,4) (11,8) (3,21) (16,0) (0,2) (11,6) (11,0) (18,17) (10,3) (15,14) (18,13) (5,13) (20,14) (2,20) (7,9) (9,22) (12,1) (17,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph615",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (18,1) (14,9) (18,11) (14,10) (3,5) (12,2) (5,12) (6,15) (7,6) (17,19) (4,5) (8,7) (6,19) (14,16) (2,0) (8,14) (12,6) (2,20) (11,15) (14,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph387",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,6) (11,9) (2,13) (8,13) (9,5) (5,8) (12,7) (16,10) (4,9) (8,16) (7,0) (10,15) (3,0) (13,12) (1,16) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1700",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,7) (21,23) (9,14) (21,16) (6,7) (3,1) (2,0) (6,20) (17,20) (5,19) (15,18) (13,15) (2,21) (3,10) (22,8) (10,16) (0,1) (10,11) (15,9) (8,6) (3,0) (14,8) (15,5) (0,5) (22,3) (14,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1437",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,18) (10,1) (15,6) (8,13) (2,15) (11,0) (18,0) (17,0) (11,3) (6,12) (1,11) (1,5) (1,0) (3,0) (2,16) (1,12) (0,2) (13,15) (17,9) (7,11) (14,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph857",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (8,15) (13,7) (14,17) (1,14) (16,7) (10,19) (24,22) (5,11) (14,10) (17,5) (11,21) (16,6) (4,23) (12,18) (21,18) (8,23) (9,3) (2,22) (19,3) (17,20) (24,23) (20,24) (13,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph668",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,12) (17,15) (20,10) (8,9) (5,10) (14,12) (9,10) (13,0) (2,11) (0,16) (7,6) (20,0) (18,11) (3,5) (6,10) (16,21) (19,5) (1,15) (14,10) (17,4) (11,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph458",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,11) (8,1) (6,17) (13,11) (6,1) (14,8) (15,17) (12,5) (2,14) (16,12) (9,5) (4,14) (2,3) (13,3) (0,4) (3,16) (14,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph285",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,4) (4,14) (8,4) (3,6) (1,9) (7,13) (6,7) (1,0) (5,0) (0,7) (1,4) (11,5) (12,1) (10,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1062",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,1) (8,4) (2,11) (3,6) (1,0) (3,2) (5,1) (11,10) (2,0) (5,12) (7,11) (9,1) (0,3) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1150",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (4,7) (7,8) (1,13) (2,4) (3,9) (5,6) (0,2) (12,13) (0,12) (14,3) (10,3) (3,11) (9,8) (4,1) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1503",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,0) (6,11) (19,8) (20,12) (15,13) (4,0) (4,5) (16,18) (19,17) (11,19) (9,1) (0,3) (17,13) (0,2) (7,3) (0,14) (4,14) (19,10) (1,2) (1,0) (11,18) (9,15) (3,14) (13,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph909",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,10) (2,6) (9,7) (7,10) (2,0) (2,1) (9,5) (3,2) (0,1) (8,3) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph815",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,7) (17,18) (9,16) (23,16) (20,1) (1,19) (12,5) (4,14) (2,22) (0,1) (1,6) (18,15) (17,4) (18,8) (20,10) (0,4) (13,16) (2,3) (2,10) (21,0) (11,18) (7,20) (9,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph806",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,21) (7,14) (18,22) (18,13) (23,11) (0,2) (3,19) (23,20) (23,16) (17,21) (5,20) (12,8) (15,4) (16,7) (4,23) (6,7) (1,13) (2,6) (9,3) (1,0) (7,8) (2,17) (10,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph215",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,8) (4,7) (5,0) (4,3) (12,2) (6,2) (9,10) (10,5) (7,1) (6,0) (4,13) (11,8) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1430",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,12) (5,18) (17,10) (3,12) (15,12) (17,1) (17,0) (12,1) (2,8) (5,7) (1,0) (13,6) (2,0) (7,16) (4,17) (11,8) (11,0) (11,14) (9,11) (12,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph357",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,0) (5,4) (4,9) (4,7) (13,9) (15,0) (0,11) (11,8) (12,1) (10,2) (3,11) (3,13) (8,10) (10,6) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph597",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,9) (11,1) (15,19) (14,18) (16,7) (0,14) (4,2) (12,14) (7,3) (15,17) (12,6) (1,2) (16,0) (15,12) (7,4) (6,10) (13,6) (11,5) (8,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph772",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,16) (11,17) (4,2) (9,12) (19,13) (4,21) (16,17) (10,1) (15,20) (22,10) (14,6) (22,18) (8,17) (6,7) (22,17) (13,5) (17,0) (16,9) (7,20) (15,3) (5,4) (21,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph468",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,7) (9,4) (0,6) (0,15) (12,15) (14,17) (10,5) (11,0) (2,14) (8,0) (13,12) (10,16) (5,17) (3,2) (4,7) (9,15) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1174",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,5) (12,4) (1,4) (8,14) (13,1) (3,0) (0,4) (10,8) (0,1) (6,3) (3,14) (13,7) (2,0) (5,12) (9,13) (11,8) (2,11) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1576",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,9) (1,19) (14,0) (5,8) (9,4) (2,20) (10,21) (6,16) (14,2) (1,7) (2,12) (3,14) (9,18) (0,1) (21,7) (13,12) (11,2) (21,20) (15,21) (19,9) (8,15) (17,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1695",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,22) (0,19) (16,2) (1,0) (12,7) (13,6) (3,20) (15,21) (5,12) (14,0) (0,2) (1,22) (8,18) (23,9) (22,4) (9,18) (21,14) (4,17) (22,20) (23,3) (5,10) (3,0) (6,11) (5,6) (21,5) (14,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph188",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,12) (8,5) (2,9) (0,6) (10,12) (4,12) (3,8) (7,9) (1,8) (12,13) (10,11) (12,9) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph467",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,0) (5,13) (14,2) (0,9) (6,11) (15,14) (0,1) (2,0) (16,8) (7,1) (1,13) (17,12) (10,3) (15,3) (17,10) (8,11) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph284",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,4) (0,8) (3,12) (12,8) (2,6) (0,11) (9,13) (14,5) (6,13) (13,7) (9,0) (1,3) (12,14) (12,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1350",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,4) (12,4) (12,17) (1,0) (6,14) (7,5) (0,16) (9,8) (3,10) (2,6) (3,9) (11,17) (11,5) (1,13) (7,0) (15,12) (13,8) (15,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1656",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,3) (1,0) (1,19) (14,3) (5,18) (19,11) (6,18) (3,8) (15,5) (10,4) (18,17) (1,16) (13,12) (2,11) (20,21) (4,5) (0,15) (21,19) (12,11) (22,3) (9,2) (3,12) (7,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1465",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,8) (6,3) (4,8) (10,18) (11,8) (10,11) (0,6) (3,0) (9,10) (5,0) (10,13) (4,0) (2,17) (16,19) (3,10) (12,14) (1,0) (13,5) (6,12) (11,7) (16,4) (2,0) (1,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph369",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,4) (9,5) (6,5) (2,1) (0,15) (9,2) (1,12) (13,1) (4,13) (3,14) (10,12) (6,15) (14,6) (4,8) (7,2) (11,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1454",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,14) (3,5) (6,5) (17,1) (2,17) (0,14) (13,16) (10,16) (14,8) (12,6) (3,14) (1,0) (11,18) (14,7) (19,17) (18,5) (19,15) (9,4) (4,2) (15,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph165",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,5) (7,8) (4,12) (1,8) (8,11) (9,3) (12,2) (2,3) (8,12) (10,9) (0,7) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph375",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,12) (0,2) (4,2) (0,6) (13,15) (8,6) (12,3) (6,14) (15,1) (7,0) (14,13) (12,2) (4,11) (10,8) (3,5) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1011",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,2) (1,0) (8,0) (3,11) (2,0) (4,1) (9,7) (5,0) (0,3) (3,2) (3,1) (4,10) (5,8) (5,6) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1026",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,7) (2,0) (5,3) (12,2) (7,6) (4,1) (5,8) (1,10) (0,1) (10,11) (7,3) (2,7) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1344",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,0) (7,0) (16,1) (16,10) (12,17) (8,12) (16,15) (8,7) (9,17) (4,7) (3,5) (7,5) (13,14) (2,0) (11,12) (17,6) (10,11) (2,17) (14,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph159",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,9) (7,6) (10,9) (8,7) (7,5) (3,2) (4,12) (8,1) (11,8) (0,7) (12,2) (8,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph658",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,3) (4,17) (1,5) (15,20) (14,8) (9,17) (10,9) (13,1) (19,6) (15,13) (12,5) (16,18) (3,15) (8,5) (5,11) (7,16) (9,6) (0,4) (15,2) (18,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph506",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,9) (16,8) (11,9) (13,17) (13,2) (3,0) (8,13) (17,5) (12,10) (7,0) (18,12) (3,15) (1,16) (14,8) (11,6) (16,10) (9,5) (7,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph852",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,12) (15,3) (24,5) (1,4) (12,13) (8,3) (15,9) (0,22) (18,6) (3,6) (24,19) (20,16) (0,15) (12,20) (24,21) (10,24) (14,15) (0,23) (19,13) (7,2) (18,4) (14,11) (22,24) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1601",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,11) (19,2) (4,19) (5,17) (14,6) (15,14) (1,0) (18,11) (8,4) (2,0) (1,8) (7,11) (14,21) (0,3) (11,13) (16,12) (16,0) (5,1) (20,5) (7,14) (10,15) (16,9) (0,4) (6,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1526",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,10) (3,0) (5,2) (14,4) (0,1) (19,2) (2,0) (13,18) (11,14) (1,3) (17,19) (16,10) (12,13) (5,3) (14,15) (17,14) (17,8) (18,16) (6,11) (10,17) (9,13) (20,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph495",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,10) (4,0) (12,17) (5,0) (7,16) (3,18) (15,0) (13,9) (18,12) (9,14) (2,1) (8,10) (11,1) (7,6) (11,12) (13,12) (11,16) (5,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph979",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,8) (0,9) (2,0) (0,3) (4,1) (6,1) (0,1) (11,9) (5,0) (2,9) (8,10) (7,3) (10,3) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph869",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,10) (14,15) (1,13) (12,13) (18,3) (10,15) (8,21) (5,1) (7,23) (8,20) (19,18) (16,22) (7,2) (11,23) (15,17) (6,0) (4,13) (1,11) (5,20) (16,15) (24,4) (1,9) (18,0) (14,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph289",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,12) (12,10) (6,0) (12,6) (12,14) (1,8) (12,4) (5,8) (8,3) (4,8) (11,14) (2,9) (9,7) (13,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1494",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,16) (7,17) (10,0) (13,14) (3,0) (4,16) (3,7) (2,6) (5,14) (5,18) (12,1) (0,12) (10,19) (14,15) (10,13) (9,0) (5,8) (0,2) (4,19) (3,4) (0,1) (6,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph819",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,2) (17,6) (18,12) (9,19) (14,0) (8,1) (11,0) (4,2) (17,3) (9,10) (12,20) (7,0) (6,8) (1,12) (23,19) (13,19) (15,20) (4,20) (0,2) (7,16) (16,22) (21,14) (19,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph105",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,9) (8,1) (9,10) (9,7) (1,4) (8,5) (1,2) (6,5) (8,0) (6,11) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1225",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,0) (7,12) (4,11) (5,4) (2,14) (8,1) (5,8) (7,5) (6,2) (9,0) (3,9) (13,4) (10,7) (13,0) (15,4) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1449",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,3) (6,4) (10,3) (5,17) (18,2) (19,16) (8,12) (3,11) (13,17) (17,15) (12,2) (11,0) (1,0) (10,14) (9,10) (4,1) (7,8) (8,0) (16,15) (0,2) (19,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph531",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,4) (11,17) (5,9) (6,2) (15,12) (17,16) (7,5) (8,2) (16,12) (12,10) (14,12) (9,15) (9,4) (10,13) (2,11) (0,2) (18,13) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1143",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,11) (9,13) (8,12) (7,6) (11,0) (3,6) (9,3) (2,7) (11,5) (13,10) (7,14) (1,9) (0,1) (4,11) (1,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph277",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,10) (7,14) (1,7) (4,10) (10,6) (0,3) (8,9) (11,2) (5,13) (7,12) (9,11) (9,4) (3,1) (5,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1617",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,9) (0,2) (2,10) (16,13) (8,19) (0,18) (3,11) (5,15) (18,8) (21,18) (16,14) (7,13) (1,17) (19,11) (17,9) (2,17) (20,6) (0,6) (0,1) (3,7) (12,20) (20,10) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph182",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,13) (9,2) (6,4) (5,13) (3,8) (2,10) (2,7) (12,10) (11,0) (10,1) (9,6) (3,2) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph814",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (20,5) (21,15) (5,4) (18,1) (23,0) (3,0) (17,5) (6,2) (2,7) (14,7) (3,5) (15,16) (9,21) (16,13) (18,0) (20,8) (11,5) (16,0) (19,8) (5,14) (10,9) (12,11) (15,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph26",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (4,2) (4,7) (1,0) (6,3) (7,6) (4,5) (8,1) (0,5) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph71",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (1,10) (8,10) (0,11) (7,4) (5,9) (10,4) (10,3) (9,2) (5,1) (2,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph472",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,9) (11,10) (16,8) (14,7) (14,1) (0,13) (11,2) (9,10) (12,15) (10,8) (13,4) (11,5) (6,3) (2,3) (5,1) (11,13) (17,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph171",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (6,12) (2,12) (0,4) (8,7) (6,1) (7,12) (8,9) (5,0) (6,10) (11,4) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1440",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,12) (14,13) (4,19) (16,11) (19,10) (0,3) (10,6) (2,6) (0,1) (7,3) (8,5) (10,0) (13,10) (0,12) (15,14) (2,0) (4,3) (18,5) (16,4) (14,5) (7,17) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1621",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,2) (16,18) (3,16) (0,2) (4,14) (11,14) (15,1) (13,14) (1,0) (21,0) (12,9) (21,7) (3,21) (14,20) (13,12) (17,11) (10,16) (19,5) (2,19) (21,19) (4,22) (9,19) (20,8) (1,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph146",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,4) (6,8) (2,9) (4,11) (3,2) (8,3) (8,1) (7,12) (7,8) (5,8) (3,10) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1199",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (8,5) (13,6) (4,6) (12,1) (4,0) (13,11) (14,10) (6,8) (2,0) (14,2) (5,14) (9,0) (4,9) (1,0) (3,12) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1456",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (3,0) (12,9) (0,2) (6,18) (8,2) (7,0) (17,4) (13,14) (16,3) (6,11) (15,16) (10,9) (4,0) (17,6) (10,5) (14,0) (18,0) (2,16) (11,19) (3,13) (3,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1666",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,0) (4,3) (12,17) (7,17) (3,10) (9,11) (18,10) (3,0) (11,7) (18,20) (15,12) (19,2) (2,0) (19,21) (6,0) (14,18) (6,7) (17,16) (21,13) (1,22) (22,14) (8,14) (6,5) (21,7) (18,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph536",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,1) (11,13) (5,14) (1,6) (1,9) (9,16) (2,0) (2,3) (8,6) (5,15) (18,5) (13,8) (13,7) (8,10) (14,4) (15,12) (14,17) (3,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph957",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,8) (1,0) (8,2) (9,0) (8,1) (7,6) (7,0) (2,0) (8,4) (2,5) (10,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph627",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (19,4) (11,4) (4,3) (10,14) (8,20) (16,10) (14,5) (7,12) (13,12) (17,6) (14,9) (6,13) (18,7) (1,9) (3,15) (2,16) (0,3) (20,12) (10,8) (19,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1586",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,21) (2,4) (12,0) (8,20) (1,0) (6,0) (3,0) (14,13) (20,18) (2,0) (13,20) (20,3) (16,8) (15,6) (12,9) (11,21) (4,19) (15,1) (6,14) (6,17) (3,5) (7,19) (10,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1770",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,12) (20,22) (20,1) (0,10) (19,1) (1,0) (2,4) (14,10) (18,9) (17,15) (0,3) (9,13) (3,9) (8,23) (21,3) (5,8) (11,8) (2,19) (13,6) (24,23) (16,2) (7,15) (8,4) (23,9) (15,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph296",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,12) (9,3) (5,9) (7,13) (8,1) (13,14) (0,13) (5,1) (13,11) (6,8) (12,14) (10,4) (2,4) (14,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1484",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,16) (11,18) (16,12) (13,4) (9,15) (2,13) (5,1) (0,17) (7,0) (0,1) (5,14) (15,16) (9,8) (6,10) (0,11) (18,13) (13,3) (15,6) (2,19) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1422",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,16) (14,13) (7,4) (17,12) (11,6) (17,14) (13,18) (5,14) (1,3) (2,10) (1,0) (11,17) (9,7) (18,8) (10,12) (6,3) (7,15) (7,18) (6,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1527",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (3,7) (16,5) (0,18) (1,0) (12,20) (12,10) (5,3) (9,13) (9,16) (7,11) (1,13) (3,6) (9,20) (16,2) (12,19) (8,5) (17,18) (4,17) (7,15) (0,2) (0,3) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph184",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,2) (5,10) (2,8) (1,13) (8,12) (0,9) (3,11) (2,5) (9,1) (4,7) (4,10) (13,2) (3,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1734",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,4) (23,1) (18,16) (0,14) (9,4) (17,2) (3,5) (1,0) (8,14) (16,15) (13,6) (3,14) (19,21) (17,7) (6,5) (1,20) (20,15) (22,20) (10,14) (22,17) (19,5) (9,14) (16,11) (12,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph70",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,6) (11,6) (4,1) (10,7) (0,2) (4,5) (7,9) (7,8) (1,7) (9,2) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph604",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,7) (17,12) (5,3) (0,10) (16,9) (18,20) (7,12) (2,19) (1,16) (17,3) (3,18) (15,7) (20,14) (15,11) (20,8) (8,4) (11,19) (1,5) (6,11) (0,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph343",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,13) (11,13) (9,14) (8,12) (9,4) (9,10) (4,3) (1,8) (6,11) (4,6) (12,0) (7,15) (15,12) (5,1) (3,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph441",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,12) (9,4) (12,14) (11,17) (2,11) (7,5) (10,17) (4,3) (16,12) (1,6) (5,9) (9,15) (2,0) (12,10) (6,2) (8,2) (15,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1692",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,14) (3,0) (1,2) (6,4) (7,11) (3,10) (0,1) (15,19) (17,19) (8,21) (11,18) (14,3) (0,2) (1,9) (22,18) (22,5) (11,19) (16,0) (23,12) (14,19) (13,16) (13,17) (9,22) (0,21) (13,12) (20,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1177",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,2) (6,10) (13,14) (11,13) (3,5) (8,12) (1,8) (6,2) (5,1) (1,10) (9,5) (0,14) (0,9) (7,0) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1121",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,4) (1,0) (13,0) (2,6) (5,2) (1,13) (11,7) (5,11) (3,7) (2,12) (9,1) (1,10) (5,8) (6,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph548",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,18) (7,2) (4,12) (7,19) (16,6) (14,1) (11,3) (13,17) (15,16) (1,2) (17,10) (6,1) (12,3) (1,8) (10,0) (9,2) (2,13) (11,18) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph8",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,2) (6,3) (0,8) (8,2) (8,7) (4,9) (5,1) (4,8) (3,8) (10,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1543",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,19) (7,20) (17,8) (0,3) (1,6) (11,9) (19,13) (3,18) (4,6) (11,12) (2,18) (15,1) (8,14) (6,5) (0,1) (13,9) (12,16) (6,14) (10,6) (0,20) (18,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph660",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (10,21) (16,14) (11,19) (21,7) (6,14) (17,8) (6,13) (11,20) (2,9) (9,10) (15,1) (10,12) (3,1) (15,18) (8,16) (17,15) (4,19) (4,17) (16,0) (12,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph207",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,13) (7,12) (5,1) (4,5) (13,2) (11,7) (7,0) (8,1) (10,9) (11,3) (5,12) (3,10) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph880",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,0) (2,11) (11,7) (23,12) (13,12) (4,17) (19,8) (11,6) (14,3) (10,19) (7,20) (18,19) (20,14) (2,15) (17,19) (2,5) (2,9) (3,1) (17,24) (9,21) (13,0) (22,16) (15,10) (16,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph371",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,10) (5,2) (2,15) (0,9) (7,8) (7,16) (11,15) (3,9) (12,1) (8,9) (10,14) (4,12) (1,7) (4,6) (13,14) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph608",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (2,17) (12,14) (19,12) (7,8) (10,7) (3,12) (7,6) (4,20) (20,11) (9,16) (13,8) (10,11) (2,14) (8,15) (5,16) (9,18) (1,19) (0,3) (3,8) (14,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1468",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (3,0) (1,5) (1,13) (13,15) (18,6) (5,12) (5,8) (3,16) (4,3) (0,2) (11,5) (0,5) (1,0) (9,10) (9,6) (3,19) (4,0) (7,16) (8,14) (15,2) (17,9) (15,18) (17,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph966",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (1,0) (11,1) (10,2) (2,4) (5,8) (11,10) (0,4) (11,7) (9,6) (0,2) (2,3) (2,8) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1476",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,11) (3,0) (13,8) (13,6) (13,18) (17,7) (4,0) (17,10) (2,0) (6,0) (9,19) (7,19) (6,2) (0,1) (16,5) (14,1) (13,5) (12,4) (1,19) (15,16) (4,15) (6,3) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1431",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,8) (15,10) (17,12) (16,7) (14,2) (18,11) (7,1) (15,9) (13,4) (12,3) (0,2) (11,17) (4,2) (7,5) (12,0) (1,0) (6,9) (1,9) (17,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1559",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,6) (1,12) (3,0) (19,9) (20,13) (11,19) (6,15) (2,14) (16,19) (20,12) (1,8) (0,20) (2,0) (7,0) (9,5) (10,0) (18,4) (2,4) (0,14) (12,17) (17,3) (7,16) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph574",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (19,10) (5,14) (14,12) (7,4) (6,4) (5,18) (8,7) (2,11) (2,7) (0,19) (19,1) (17,5) (15,3) (8,1) (3,11) (16,10) (1,13) (13,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1538",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,0) (15,10) (13,9) (4,3) (8,17) (12,11) (11,20) (8,16) (3,8) (7,0) (17,0) (13,6) (9,5) (1,0) (0,3) (11,13) (0,19) (2,5) (18,13) (0,2) (19,15) (1,17) (9,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph699",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,11) (13,12) (5,2) (15,21) (10,19) (11,7) (9,17) (2,9) (0,1) (8,19) (2,15) (18,16) (17,4) (11,16) (12,19) (14,20) (14,3) (11,6) (3,1) (7,20) (13,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph168",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,3) (7,3) (1,4) (10,7) (11,10) (3,5) (5,8) (2,12) (7,2) (1,10) (7,6) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph972",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,9) (9,10) (5,7) (5,2) (8,3) (4,7) (0,6) (8,5) (6,9) (11,4) (0,1) (0,4) (0,5) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1154",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,9) (4,12) (0,4) (3,0) (1,13) (10,4) (12,8) (1,0) (3,11) (3,14) (6,11) (13,6) (2,0) (0,5) (14,8) (2,8) (7,10) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1625",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (2,17) (19,13) (0,2) (11,18) (7,21) (10,2) (6,16) (1,6) (16,18) (4,0) (17,22) (8,20) (1,15) (1,0) (0,3) (7,2) (5,4) (14,3) (13,20) (2,1) (17,12) (1,9) (2,13) (0,10) (3,11) (4,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1140",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (1,0) (1,3) (0,13) (7,14) (2,0) (6,11) (12,4) (4,11) (11,9) (4,1) (6,14) (3,5) (14,0) (13,2) (13,10) (10,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph662",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (19,5) (21,18) (11,16) (5,13) (1,18) (19,6) (9,8) (17,1) (21,10) (0,1) (13,20) (6,15) (4,2) (11,2) (16,12) (2,3) (8,19) (7,5) (11,21) (9,14) (20,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph393",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,7) (2,9) (15,10) (13,11) (0,16) (1,3) (11,4) (14,6) (15,14) (8,4) (1,15) (9,6) (16,8) (16,12) (12,14) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1776",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,6) (18,24) (22,2) (0,14) (9,23) (4,0) (11,2) (24,23) (17,23) (22,16) (3,13) (18,0) (13,14) (3,16) (8,0) (21,12) (0,1) (19,20) (20,9) (16,15) (24,10) (5,17) (23,7) (12,3) (1,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph87",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,0) (4,9) (9,6) (11,4) (10,8) (3,5) (2,6) (4,8) (3,2) (7,11) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph414",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,10) (2,7) (16,1) (14,15) (5,1) (10,2) (3,1) (0,6) (8,5) (13,4) (8,13) (16,7) (0,11) (15,9) (14,6) (12,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph411",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,7) (0,3) (6,8) (11,10) (2,0) (14,7) (7,11) (14,9) (15,12) (2,16) (10,5) (13,3) (1,6) (13,14) (4,3) (6,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1115",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,4) (11,12) (7,5) (10,2) (6,3) (0,1) (3,0) (0,5) (1,5) (0,2) (10,1) (11,7) (9,1) (11,8) (6,12) (13,0) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph974",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,1) (1,0) (4,11) (2,7) (1,7) (7,11) (11,9) (0,4) (2,6) (5,8) (3,0) (5,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1152",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,6) (2,0) (11,10) (12,11) (8,2) (4,0) (5,10) (7,9) (3,0) (2,7) (1,7) (5,13) (1,12) (11,4) (9,14) (1,0) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph422",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,9) (9,14) (10,8) (8,6) (3,11) (4,0) (15,5) (15,13) (2,10) (6,17) (6,0) (0,16) (11,2) (1,17) (7,3) (12,16) (7,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph307",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,2) (1,10) (12,5) (7,3) (5,14) (15,13) (1,11) (8,6) (4,13) (5,8) (13,5) (1,0) (5,0) (10,2) (3,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph706",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (18,8) (10,7) (6,11) (15,21) (17,1) (0,11) (16,17) (14,15) (20,3) (13,5) (20,2) (3,10) (2,0) (18,12) (6,4) (7,21) (11,8) (0,13) (9,1) (19,14) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1247",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,5) (9,5) (4,3) (8,6) (3,2) (0,2) (13,11) (10,15) (13,0) (2,12) (15,14) (7,3) (13,14) (8,10) (1,4) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1585",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (12,4) (0,21) (12,0) (14,16) (2,0) (6,21) (10,4) (0,3) (17,7) (1,0) (19,20) (2,8) (11,13) (15,8) (21,19) (0,17) (11,9) (8,20) (19,14) (1,15) (15,11) (3,21) (7,18) (16,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1209",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,9) (13,8) (11,1) (4,12) (12,14) (15,5) (7,0) (3,10) (1,0) (3,0) (13,6) (4,1) (7,5) (2,0) (2,6) (9,3) (6,15) (12,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1541",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,10) (1,3) (15,13) (1,0) (19,3) (6,19) (14,17) (1,17) (13,7) (20,18) (8,15) (20,17) (9,18) (7,12) (16,2) (5,17) (5,11) (16,11) (4,3) (10,14) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph469",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,7) (8,10) (14,9) (13,16) (16,11) (10,13) (12,11) (9,4) (3,8) (8,17) (16,5) (8,4) (6,12) (3,2) (3,15) (1,16) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1726",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (20,22) (16,8) (1,0) (6,9) (1,15) (9,13) (19,17) (5,12) (0,2) (8,11) (8,10) (14,2) (7,21) (2,6) (0,20) (3,22) (5,7) (4,8) (15,2) (12,11) (23,2) (18,23) (18,20) (17,10) (7,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1784",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (13,0) (24,6) (20,18) (4,10) (21,7) (22,13) (18,14) (3,0) (9,24) (0,5) (20,16) (3,4) (10,15) (1,23) (21,8) (0,1) (10,19) (2,3) (8,12) (6,13) (2,23) (13,14) (4,11) (2,0) (21,5) (18,15) (3,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1098",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,13) (12,3) (8,11) (12,6) (1,11) (9,4) (2,0) (13,6) (2,4) (3,0) (5,10) (2,13) (9,7) (1,2) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1593",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (5,8) (6,2) (7,3) (14,17) (20,9) (3,0) (6,10) (10,13) (20,7) (5,19) (1,0) (18,4) (10,0) (14,13) (0,15) (14,5) (4,19) (10,21) (16,12) (12,1) (3,4) (11,0) (16,21) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1557",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,2) (9,16) (12,14) (12,3) (3,8) (6,7) (1,0) (11,20) (2,14) (10,7) (13,8) (10,11) (9,18) (2,17) (20,4) (8,7) (8,15) (4,0) (19,12) (5,16) (9,14) (19,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph917",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,8) (10,0) (3,7) (1,0) (1,3) (3,6) (0,9) (0,5) (6,9) (2,4) (6,4) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1616",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,3) (9,15) (8,0) (20,8) (2,10) (7,14) (15,0) (6,11) (7,10) (19,13) (1,8) (0,16) (4,7) (4,17) (15,21) (1,0) (16,19) (21,18) (12,17) (6,5) (17,20) (6,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph415",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,11) (14,13) (3,14) (15,11) (9,15) (8,3) (4,14) (0,10) (1,9) (12,5) (13,12) (16,0) (5,16) (6,4) (13,11) (1,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph67",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (6,7) (4,11) (11,10) (1,2) (4,3) (0,1) (1,5) (7,8) (2,10) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1499",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,8) (4,19) (10,16) (14,9) (3,4) (10,14) (0,4) (7,12) (14,5) (16,2) (11,4) (1,0) (17,6) (3,0) (13,6) (18,7) (15,3) (8,19) (2,12) (0,2) (12,13) (1,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph181",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,5) (9,1) (6,11) (10,8) (0,13) (11,10) (0,8) (13,7) (11,3) (5,4) (9,11) (4,2) (13,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph749",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,6) (7,8) (8,17) (3,15) (11,7) (21,4) (1,11) (2,15) (5,9) (9,20) (18,20) (4,22) (10,21) (12,14) (7,0) (10,9) (14,0) (21,13) (7,19) (13,15) (22,16) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph232",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,12) (2,9) (4,2) (7,10) (0,1) (6,9) (8,11) (11,1) (2,10) (7,12) (2,3) (3,11) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1414",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,16) (10,12) (13,8) (14,8) (9,4) (0,2) (13,2) (6,11) (0,3) (16,10) (18,12) (9,11) (5,9) (0,1) (5,17) (16,8) (7,0) (15,3) (17,13) (7,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph589",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,9) (13,8) (14,9) (3,8) (7,8) (5,7) (9,17) (2,16) (3,12) (6,8) (0,3) (10,7) (2,14) (1,19) (19,11) (12,14) (11,10) (12,18) (16,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1747",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,0) (0,1) (16,4) (12,11) (5,11) (2,20) (4,24) (8,11) (4,0) (9,13) (17,12) (10,9) (16,18) (18,6) (8,3) (3,22) (19,0) (3,10) (2,0) (15,7) (0,14) (19,11) (18,21) (13,2) (23,4) (0,7) (24,0) (1,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph762",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,15) (1,4) (18,10) (9,18) (6,0) (2,17) (18,12) (8,9) (13,9) (21,7) (11,2) (14,18) (19,11) (14,20) (1,22) (16,20) (8,11) (4,17) (6,15) (5,2) (15,21) (22,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph229",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,8) (8,6) (2,10) (11,7) (9,13) (11,5) (8,12) (0,2) (13,12) (1,12) (12,2) (8,3) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1285",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,1) (16,12) (15,0) (2,0) (3,0) (13,11) (14,7) (4,0) (14,16) (8,6) (9,13) (1,0) (0,7) (4,6) (12,10) (5,9) (3,2) (11,4) (8,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1797",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,13) (24,15) (22,3) (14,5) (4,19) (6,2) (21,4) (0,1) (0,10) (3,7) (17,0) (6,10) (0,11) (16,12) (14,13) (14,20) (23,7) (12,1) (20,9) (24,10) (22,16) (5,19) (8,5) (21,18) (2,0) (22,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph454",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,10) (12,4) (9,13) (15,13) (17,1) (1,3) (14,0) (6,16) (11,5) (8,2) (14,11) (4,5) (8,11) (17,16) (1,0) (7,15) (13,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph121",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,5) (3,6) (11,2) (5,12) (11,10) (4,2) (3,2) (11,7) (1,9) (4,8) (1,0) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph747",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,0) (4,20) (19,22) (0,12) (18,6) (17,10) (3,5) (14,6) (7,19) (9,12) (11,21) (21,20) (2,4) (20,17) (16,8) (20,3) (15,6) (22,8) (14,13) (15,1) (0,22) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph466",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,0) (11,5) (12,17) (8,9) (6,14) (16,0) (13,1) (15,12) (8,13) (7,5) (3,10) (11,17) (6,2) (4,1) (12,4) (3,9) (6,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1799",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,0) (18,13) (4,1) (0,4) (11,22) (8,17) (18,2) (8,23) (2,0) (7,8) (13,20) (5,7) (9,6) (0,16) (0,3) (2,9) (15,13) (0,5) (12,24) (16,5) (20,21) (20,14) (3,10) (10,0) (2,17) (11,17) (19,23) (15,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1584",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,14) (21,17) (7,19) (3,18) (17,5) (20,12) (6,7) (6,15) (0,16) (20,17) (7,1) (19,10) (17,8) (19,2) (4,11) (0,15) (13,18) (4,9) (1,0) (11,15) (8,18) (15,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph368",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,8) (7,10) (0,8) (2,5) (6,14) (8,9) (1,13) (16,10) (13,2) (15,3) (4,11) (12,14) (3,0) (0,13) (1,12) (11,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph730",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,13) (20,7) (9,5) (12,1) (22,10) (1,8) (20,3) (18,3) (21,18) (21,6) (18,9) (9,1) (19,16) (19,10) (18,17) (6,16) (15,13) (6,0) (11,15) (12,2) (14,8) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph103",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,9) (6,2) (2,4) (8,4) (5,11) (2,1) (1,10) (5,6) (9,3) (1,0) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph532",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,13) (16,9) (18,2) (6,15) (13,5) (14,15) (11,9) (7,8) (2,1) (17,3) (15,0) (1,9) (2,8) (8,4) (12,10) (0,10) (3,9) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph623",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (18,9) (17,13) (7,5) (15,7) (0,6) (7,10) (2,3) (17,12) (7,18) (18,14) (19,1) (11,8) (20,19) (14,19) (18,17) (14,6) (10,3) (16,19) (12,11) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph24",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (9,3) (6,4) (3,7) (10,6) (1,5) (0,7) (5,7) (2,7) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1368",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (17,8) (3,4) (1,0) (9,10) (11,2) (14,7) (9,13) (3,8) (16,4) (16,15) (1,16) (0,6) (2,13) (11,5) (0,7) (10,3) (11,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1359",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (10,2) (13,4) (12,15) (2,0) (7,17) (5,13) (14,2) (16,3) (1,0) (11,8) (3,0) (1,15) (5,17) (6,16) (5,0) (3,8) (5,16) (9,17) (1,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1215",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,7) (14,2) (1,15) (2,12) (6,9) (14,0) (4,9) (9,1) (2,9) (0,1) (2,11) (8,2) (6,13) (8,5) (12,10) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1012",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (8,3) (2,10) (0,3) (0,2) (4,0) (0,1) (8,7) (7,0) (8,1) (0,5) (9,0) (8,5) (9,11) (11,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph970",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (3,1) (7,0) (1,10) (10,0) (4,2) (2,0) (11,4) (0,1) (10,11) (6,7) (5,3) (9,0) (0,4) (8,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph86",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,8) (4,7) (10,9) (8,5) (10,3) (3,0) (11,3) (1,7) (2,9) (6,0) (10,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph619",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (10,20) (14,11) (15,6) (0,3) (17,12) (17,2) (20,6) (6,19) (8,5) (13,14) (19,4) (18,6) (5,12) (1,4) (19,3) (4,5) (4,7) (9,7) (4,16) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph157",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,8) (5,11) (2,12) (3,12) (4,0) (11,1) (9,0) (7,5) (1,10) (0,12) (8,12) (8,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph533",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,7) (4,5) (10,4) (1,16) (15,5) (11,3) (9,2) (0,15) (1,17) (18,6) (18,12) (14,3) (5,18) (2,11) (8,3) (13,12) (17,3) (11,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1165",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (5,14) (12,8) (0,8) (13,7) (5,4) (0,2) (6,13) (14,12) (6,2) (12,3) (0,9) (10,12) (13,9) (1,0) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1551",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,5) (2,0) (3,0) (2,3) (19,2) (13,14) (10,4) (3,4) (20,8) (10,11) (13,17) (10,15) (18,14) (13,0) (4,1) (18,15) (18,12) (7,8) (6,20) (13,6) (3,9) (1,0) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1082",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,4) (4,6) (8,2) (12,0) (8,3) (13,5) (7,5) (2,1) (9,4) (13,1) (0,10) (7,10) (1,0) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1792",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,10) (11,5) (0,14) (9,13) (2,0) (12,17) (2,13) (1,16) (11,8) (3,22) (0,3) (1,0) (0,24) (2,20) (18,6) (19,0) (19,11) (23,4) (9,10) (7,0) (4,24) (21,18) (3,8) (7,15) (11,12) (16,18) (16,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1689",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (22,6) (17,13) (8,13) (18,16) (19,1) (4,17) (11,10) (12,14) (20,17) (12,17) (1,0) (15,11) (0,23) (11,9) (22,19) (12,7) (12,1) (8,2) (12,3) (16,5) (18,0) (7,21) (7,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph843",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (14,8) (6,7) (21,15) (12,17) (7,17) (3,4) (18,11) (24,9) (5,6) (20,17) (19,18) (7,24) (19,2) (24,18) (1,22) (6,0) (24,10) (23,19) (21,18) (3,10) (13,11) (7,14) (12,16) (21,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph761",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (20,13) (6,12) (7,11) (11,10) (19,10) (18,0) (6,3) (1,17) (15,12) (8,4) (20,2) (3,10) (8,11) (8,2) (1,22) (21,10) (22,16) (9,10) (14,21) (4,16) (0,5) (13,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1415",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (10,3) (1,15) (11,7) (5,13) (12,6) (10,11) (1,0) (6,3) (2,8) (14,12) (17,10) (2,0) (4,8) (18,4) (10,13) (16,2) (0,6) (4,0) (0,5) (10,9) (11,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph408",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,2) (2,15) (11,10) (4,15) (1,0) (1,9) (15,8) (3,16) (3,13) (14,11) (6,15) (7,8) (12,4) (0,8) (0,10) (6,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1452",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,13) (0,5) (17,16) (1,0) (1,18) (9,17) (0,12) (1,15) (5,17) (8,2) (19,0) (3,6) (10,4) (2,0) (0,4) (11,15) (0,3) (14,2) (8,6) (19,3) (6,18) (16,7) (19,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph91",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,11) (9,5) (2,5) (4,5) (1,9) (7,11) (4,11) (6,2) (8,10) (9,8) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1727",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,9) (0,15) (8,23) (18,6) (14,10) (0,2) (0,1) (23,22) (13,19) (11,15) (0,22) (15,3) (2,5) (2,8) (20,12) (4,1) (16,20) (12,13) (21,14) (12,17) (19,0) (18,4) (8,14) (7,3) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1208",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,13) (4,8) (3,14) (15,0) (2,0) (5,6) (10,1) (9,5) (0,3) (2,1) (13,15) (12,6) (9,2) (2,7) (0,1) (12,4) (6,14) (11,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1618",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,14) (2,5) (8,9) (4,6) (13,1) (4,21) (11,15) (18,16) (10,1) (17,4) (16,15) (6,2) (7,15) (16,1) (0,19) (19,11) (0,12) (9,7) (20,10) (0,17) (1,0) (10,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1381",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,11) (6,7) (2,5) (2,0) (18,12) (16,11) (5,14) (1,18) (4,12) (5,3) (13,14) (6,15) (14,9) (14,10) (8,7) (17,6) (14,8) (3,0) (6,12) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph335",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,7) (11,0) (12,0) (12,7) (8,2) (1,12) (11,8) (7,13) (11,10) (11,6) (14,1) (3,12) (13,4) (15,5) (9,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1620",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,8) (20,7) (19,16) (13,15) (1,9) (20,3) (0,6) (1,0) (15,11) (9,18) (12,2) (21,6) (4,0) (16,6) (18,21) (18,3) (13,3) (19,10) (1,8) (22,10) (12,1) (18,17) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph695",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,8) (1,3) (19,2) (4,14) (1,6) (16,19) (4,21) (17,9) (12,14) (7,11) (11,13) (20,17) (14,18) (5,3) (13,15) (10,16) (18,13) (17,14) (10,17) (5,2) (21,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph790",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,10) (9,13) (16,18) (6,11) (22,0) (15,6) (14,17) (4,3) (1,19) (19,0) (3,14) (21,14) (3,12) (5,10) (23,22) (16,8) (9,5) (16,19) (14,5) (7,10) (3,11) (16,2) (8,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1007",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,6) (2,3) (9,10) (0,2) (8,3) (3,0) (1,0) (4,0) (0,11) (7,2) (11,10) (3,6) (2,10) (9,4) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph617",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,8) (7,18) (2,10) (1,12) (9,17) (5,20) (0,17) (4,14) (19,4) (12,18) (6,5) (11,12) (0,7) (15,9) (18,13) (8,16) (10,5) (0,14) (10,4) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph433",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,7) (3,13) (15,0) (11,12) (4,9) (11,6) (3,12) (1,17) (10,12) (5,1) (11,16) (14,5) (11,2) (2,8) (5,4) (3,17) (3,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph723",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,0) (0,19) (8,15) (1,17) (19,6) (5,17) (16,19) (4,10) (20,21) (16,7) (13,4) (18,16) (20,6) (0,12) (3,20) (2,14) (17,9) (8,6) (3,22) (20,2) (18,1) (15,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph558",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (19,15) (14,0) (11,5) (0,16) (7,3) (17,15) (13,6) (4,2) (4,9) (16,7) (4,7) (6,12) (15,12) (12,8) (2,1) (6,10) (14,12) (14,18) (1,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1194",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (10,5) (6,3) (1,0) (14,8) (4,12) (7,13) (11,2) (11,8) (4,0) (5,12) (4,1) (9,13) (1,13) (10,8) (3,0) (3,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph848",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,9) (21,16) (7,13) (18,0) (16,22) (7,17) (3,7) (17,4) (8,3) (2,16) (1,13) (14,9) (24,12) (0,15) (3,5) (5,10) (18,19) (23,9) (24,5) (6,22) (12,11) (20,12) (22,20) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph97",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,7) (3,6) (4,5) (10,4) (7,1) (4,8) (0,5) (9,1) (0,1) (11,7) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph666",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,11) (4,7) (10,7) (4,5) (17,3) (0,6) (3,1) (6,19) (2,4) (13,14) (5,9) (6,16) (21,0) (19,8) (5,12) (4,17) (20,6) (6,13) (4,19) (14,15) (12,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph731",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (16,11) (13,19) (6,15) (8,4) (15,14) (16,19) (20,22) (18,0) (16,17) (7,3) (9,21) (10,18) (7,20) (8,17) (2,20) (5,1) (14,9) (21,20) (5,12) (21,10) (15,16) (5,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph997",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,2) (9,11) (8,5) (2,0) (3,0) (1,0) (4,11) (0,4) (7,8) (7,0) (2,6) (8,1) (3,8) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1263",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,14) (1,0) (7,3) (3,4) (7,15) (5,8) (9,0) (0,10) (5,14) (12,0) (4,13) (16,14) (2,6) (4,5) (0,2) (16,11) (12,1) (6,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1560",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,12) (20,7) (20,8) (0,2) (6,5) (16,1) (14,8) (0,4) (1,6) (3,18) (11,12) (18,2) (1,0) (6,4) (6,10) (21,15) (9,11) (15,0) (19,13) (19,14) (9,13) (9,18) (0,3) (14,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1781",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,21) (21,3) (12,0) (15,1) (21,6) (2,8) (0,2) (20,22) (19,22) (13,12) (1,0) (4,19) (16,5) (24,14) (11,16) (21,0) (11,15) (10,4) (14,4) (17,7) (0,3) (11,9) (20,8) (18,14) (23,7) (15,8) (0,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1190",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,2) (2,0) (13,1) (1,0) (10,3) (11,8) (5,0) (13,12) (6,8) (5,8) (3,13) (4,8) (4,0) (0,3) (13,9) (7,2) (14,4) (13,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph566",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,9) (14,0) (3,8) (4,16) (6,18) (15,7) (12,0) (18,17) (16,1) (7,0) (3,10) (8,19) (2,13) (2,11) (11,5) (13,9) (16,18) (12,11) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph629",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,8) (2,6) (10,8) (14,20) (16,0) (1,19) (8,2) (16,11) (12,4) (15,16) (19,0) (3,10) (16,6) (1,17) (0,9) (14,11) (6,18) (16,5) (19,7) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph12",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,2) (0,10) (4,3) (6,3) (8,7) (2,6) (8,9) (0,4) (6,5) (1,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1418",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (12,15) (9,4) (7,5) (12,10) (4,3) (17,11) (17,16) (11,2) (1,6) (9,15) (12,16) (6,2) (5,9) (10,13) (2,8) (1,0) (18,13) (12,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph823",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,21) (1,4) (15,12) (13,1) (6,0) (11,1) (18,17) (13,23) (13,9) (14,15) (1,5) (6,14) (15,16) (10,15) (23,7) (8,20) (8,19) (5,20) (10,2) (0,18) (2,7) (18,3) (22,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph796",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,23) (4,21) (21,23) (1,9) (13,17) (8,7) (0,8) (21,17) (11,10) (16,15) (5,2) (2,15) (8,15) (0,1) (22,17) (13,20) (18,14) (4,12) (0,10) (6,15) (23,6) (19,11) (3,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1252",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,11) (11,5) (13,7) (2,0) (2,9) (14,6) (11,0) (6,12) (1,12) (9,13) (0,1) (4,1) (15,2) (11,3) (15,0) (3,0) (10,15) (1,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph113",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (2,4) (3,7) (1,2) (9,10) (8,5) (11,0) (4,6) (8,2) (0,2) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1173",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,7) (4,9) (0,1) (13,14) (10,4) (7,9) (0,4) (3,0) (4,14) (12,6) (1,12) (6,7) (9,11) (0,2) (3,6) (5,0) (6,8) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1117",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,7) (10,7) (3,2) (1,13) (7,0) (6,12) (5,13) (13,8) (7,11) (0,1) (8,4) (3,9) (9,12) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1315",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,11) (15,2) (12,6) (0,15) (11,0) (4,1) (12,1) (5,11) (10,15) (7,13) (11,3) (9,2) (8,1) (9,13) (0,16) (0,1) (14,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1256",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,0) (13,0) (7,0) (12,10) (5,0) (1,8) (7,14) (6,8) (1,12) (4,11) (12,14) (4,2) (15,2) (9,3) (0,2) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph685",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (21,12) (5,4) (3,14) (8,3) (14,4) (0,15) (18,20) (11,18) (6,11) (19,17) (19,9) (13,17) (16,0) (13,12) (21,7) (2,1) (13,16) (11,19) (1,9) (15,10) (14,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1423",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,11) (15,18) (13,14) (15,10) (13,0) (4,10) (9,18) (1,0) (13,12) (8,6) (5,0) (7,3) (1,4) (10,8) (14,17) (4,3) (18,13) (2,16) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph736",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,2) (8,7) (20,6) (7,22) (22,9) (15,17) (13,10) (0,15) (11,3) (20,17) (1,8) (11,10) (19,21) (7,18) (2,17) (4,11) (12,15) (5,11) (10,16) (4,2) (21,3) (7,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph656",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,19) (16,12) (3,18) (13,9) (15,1) (18,9) (6,10) (0,20) (14,6) (17,8) (14,19) (7,20) (6,5) (6,1) (3,0) (14,8) (6,4) (11,9) (18,2) (12,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1579",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,19) (16,20) (1,16) (17,14) (0,2) (10,18) (11,12) (9,12) (13,17) (12,8) (4,7) (0,7) (21,18) (6,17) (17,16) (8,21) (5,3) (7,5) (15,14) (11,20) (7,8) (17,2) (0,1) (3,0) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1316",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,7) (5,11) (1,10) (12,2) (16,6) (1,0) (9,15) (5,15) (5,14) (1,13) (2,10) (16,3) (16,5) (5,0) (2,0) (13,4) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph167",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,11) (12,3) (4,3) (9,2) (0,12) (4,2) (8,9) (7,10) (4,1) (0,5) (6,4) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph721",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,18) (1,22) (3,22) (9,8) (4,17) (11,19) (14,20) (21,7) (2,11) (9,18) (8,15) (21,15) (2,17) (1,4) (10,18) (20,16) (13,9) (0,6) (12,18) (2,5) (11,8) (15,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph96",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (7,5) (8,11) (7,0) (5,1) (7,10) (6,10) (4,5) (1,8) (11,3) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph572",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,11) (9,13) (1,10) (4,15) (11,14) (17,12) (5,4) (16,6) (13,5) (14,19) (0,1) (15,7) (11,5) (0,18) (17,1) (2,8) (14,12) (16,13) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph521",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (17,2) (5,10) (7,11) (8,18) (4,12) (17,13) (9,3) (8,1) (14,7) (6,9) (0,8) (4,5) (13,4) (2,15) (7,5) (0,9) (16,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph710",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,15) (1,11) (21,19) (1,9) (17,3) (6,0) (12,8) (18,15) (4,0) (9,18) (16,6) (6,20) (20,7) (21,18) (12,2) (13,14) (5,9) (16,19) (18,3) (1,8) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1609",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,21) (7,12) (16,4) (6,17) (21,6) (1,4) (11,8) (20,1) (9,21) (3,18) (3,0) (20,13) (14,0) (18,4) (9,7) (11,19) (0,1) (0,16) (2,0) (2,14) (1,10) (6,20) (14,8) (16,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1534",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,1) (17,14) (2,0) (12,6) (0,15) (1,9) (15,4) (4,10) (7,4) (1,19) (13,4) (14,16) (17,7) (3,5) (4,0) (7,12) (0,1) (3,0) (18,1) (11,3) (17,3) (8,4) (16,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph312",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,12) (3,8) (5,1) (13,15) (13,2) (14,4) (14,3) (12,14) (11,6) (1,4) (7,14) (2,0) (1,2) (10,9) (11,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph162",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,2) (11,6) (10,7) (2,8) (4,12) (5,7) (0,10) (4,1) (4,9) (6,0) (5,4) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph577",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,11) (13,17) (18,15) (7,6) (1,13) (4,3) (3,5) (0,2) (19,16) (0,9) (7,16) (2,14) (4,12) (17,3) (7,8) (10,8) (18,19) (6,2) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph163",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,6) (8,1) (3,7) (4,5) (0,10) (7,6) (8,5) (7,12) (2,0) (9,8) (2,7) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1058",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (3,0) (5,4) (8,12) (0,8) (2,4) (8,11) (1,6) (6,4) (2,0) (12,2) (11,10) (11,9) (5,7) (12,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1581",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (11,21) (15,17) (19,20) (0,2) (1,0) (18,14) (3,2) (10,3) (7,10) (4,6) (8,11) (7,21) (14,6) (16,7) (18,17) (6,0) (21,14) (7,5) (12,17) (19,18) (9,18) (12,13) (3,0) (19,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph407",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,1) (15,7) (13,5) (2,11) (2,0) (16,9) (14,1) (3,10) (6,3) (10,16) (1,12) (1,16) (14,4) (4,8) (7,9) (8,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph42",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,4) (1,4) (0,1) (6,8) (1,9) (0,10) (2,7) (6,7) (2,1) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph328",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,10) (9,0) (13,7) (11,0) (5,14) (3,7) (2,6) (14,10) (6,10) (12,4) (4,3) (15,14) (12,1) (5,8) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1433",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,12) (9,12) (4,9) (17,18) (14,2) (14,7) (10,18) (0,1) (6,1) (7,11) (17,3) (16,6) (12,6) (10,13) (5,15) (15,17) (15,8) (15,1) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph633",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,16) (11,2) (5,7) (17,11) (17,20) (13,5) (2,4) (14,6) (1,18) (19,6) (13,20) (0,1) (1,15) (8,19) (2,3) (12,19) (10,9) (16,12) (9,8) (18,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph554",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,5) (6,2) (7,17) (15,14) (5,18) (10,13) (19,10) (1,12) (3,7) (16,11) (9,0) (16,4) (12,0) (3,4) (10,0) (6,10) (4,19) (13,14) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph479",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,10) (9,12) (11,8) (6,12) (11,4) (1,0) (10,7) (2,15) (2,8) (3,6) (10,3) (16,10) (13,5) (10,11) (5,0) (8,17) (1,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph149",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,4) (8,9) (4,0) (6,1) (0,5) (4,11) (8,7) (12,2) (12,7) (6,10) (3,6) (12,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph40",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,0) (7,2) (0,3) (5,9) (8,10) (6,8) (6,7) (10,1) (4,1) (3,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1667",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,17) (21,10) (4,3) (17,8) (8,3) (22,14) (11,13) (21,0) (14,11) (5,9) (0,1) (13,6) (5,2) (20,13) (11,15) (18,19) (9,13) (16,9) (13,0) (8,19) (7,0) (15,12) (0,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1155",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,13) (4,2) (11,5) (2,8) (9,0) (14,0) (0,1) (7,12) (4,9) (5,3) (2,12) (4,6) (11,10) (3,0) (8,1) (2,0) (5,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1425",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,18) (14,18) (5,3) (10,15) (13,9) (2,4) (16,17) (1,3) (0,2) (17,14) (17,10) (16,13) (5,10) (12,14) (1,0) (11,2) (8,14) (17,6) (7,13) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1254",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,10) (11,4) (15,8) (5,2) (1,12) (0,1) (8,0) (13,0) (14,6) (12,11) (13,2) (1,13) (9,8) (3,0) (7,10) (3,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph365",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,0) (7,11) (4,12) (4,3) (10,8) (13,14) (0,2) (7,16) (1,13) (16,15) (3,5) (1,0) (8,7) (3,2) (6,2) (6,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph556",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,14) (19,3) (12,5) (6,17) (7,4) (5,8) (4,15) (18,6) (14,10) (11,13) (4,19) (3,0) (6,13) (6,19) (2,17) (4,5) (4,1) (16,12) (7,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph584",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,6) (9,1) (14,0) (13,9) (2,0) (4,11) (19,0) (2,3) (7,19) (13,12) (10,9) (12,16) (18,14) (0,16) (14,8) (17,7) (6,8) (15,11) (18,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph90",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (6,3) (11,9) (3,1) (9,8) (5,3) (2,5) (4,7) (7,8) (1,4) (10,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1005",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,1) (11,4) (8,5) (2,0) (3,6) (5,6) (3,0) (0,8) (2,10) (1,0) (0,7) (3,10) (1,9) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph732",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,19) (1,10) (21,9) (18,4) (6,19) (14,0) (7,9) (21,11) (2,14) (6,17) (11,8) (6,20) (20,1) (4,16) (8,14) (5,16) (18,3) (12,7) (20,13) (1,4) (16,0) (15,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph16",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,3) (0,9) (10,5) (10,2) (4,7) (6,5) (2,8) (1,7) (5,0) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph526",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,12) (14,7) (6,16) (6,12) (1,15) (15,5) (10,13) (18,10) (11,7) (0,4) (14,12) (4,9) (2,14) (6,1) (17,18) (17,15) (15,8) (3,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1420",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,17) (4,0) (3,0) (15,5) (0,6) (18,0) (8,18) (0,2) (0,1) (2,11) (8,10) (9,17) (16,6) (12,16) (2,10) (17,1) (3,7) (15,13) (11,3) (13,7) (9,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph832",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,21) (22,17) (10,20) (0,8) (3,11) (9,8) (12,2) (13,10) (12,8) (17,6) (20,14) (15,2) (22,23) (1,4) (4,23) (11,0) (16,19) (6,5) (22,19) (17,18) (22,10) (15,16) (3,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph622",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (2,4) (5,11) (7,14) (14,18) (15,5) (14,13) (6,13) (4,16) (14,20) (10,7) (12,9) (17,3) (2,0) (8,9) (11,2) (9,1) (16,19) (13,5) (8,17) (15,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1066",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,6) (0,1) (10,4) (6,0) (0,2) (9,8) (7,12) (11,2) (4,3) (5,0) (7,1) (5,7) (8,10) (5,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1645",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (9,20) (2,16) (9,18) (8,5) (20,1) (2,0) (14,10) (8,11) (2,19) (2,4) (4,8) (12,2) (6,13) (9,13) (15,7) (15,0) (19,1) (10,0) (1,0) (3,9) (3,0) (4,0) (3,21) (8,22) (17,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph924",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,4) (7,5) (3,10) (2,0) (9,0) (1,2) (3,0) (1,0) (6,5) (3,8) (3,2) (2,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph680",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,10) (6,16) (15,14) (11,15) (21,17) (19,3) (12,9) (0,12) (6,18) (17,8) (19,8) (12,13) (16,7) (1,5) (20,9) (8,1) (18,11) (13,2) (4,3) (9,4) (4,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph872",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,16) (9,13) (1,15) (19,8) (11,3) (3,23) (23,1) (14,18) (10,4) (0,17) (8,13) (21,22) (7,23) (11,24) (18,24) (9,4) (12,10) (16,24) (20,11) (4,6) (8,20) (18,22) (5,24) (10,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1211",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,10) (9,4) (15,7) (5,2) (12,3) (6,2) (0,3) (1,15) (10,13) (2,0) (11,15) (14,11) (4,6) (10,1) (0,1) (0,9) (7,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph358",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,9) (6,9) (13,1) (15,2) (4,15) (1,5) (12,8) (0,4) (11,5) (9,4) (6,3) (13,15) (14,3) (10,5) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1321",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (11,9) (9,13) (8,14) (0,13) (11,12) (8,17) (9,5) (16,13) (2,5) (0,15) (4,3) (13,6) (10,15) (0,7) (3,8) (17,1) (0,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph647",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (19,11) (5,0) (10,12) (10,7) (8,16) (1,3) (6,14) (1,15) (9,2) (11,18) (6,9) (0,16) (16,14) (17,15) (14,12) (17,8) (20,10) (4,19) (13,15) (4,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1736",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (10,1) (12,6) (21,1) (4,15) (17,7) (23,18) (8,4) (3,5) (16,4) (1,0) (22,14) (3,12) (1,19) (21,20) (17,3) (7,4) (4,1) (21,9) (22,23) (0,15) (3,0) (4,0) (4,11) (7,13) (23,17) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1467",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (16,10) (17,13) (0,1) (8,19) (0,7) (15,14) (7,8) (12,11) (16,1) (0,2) (9,12) (3,5) (14,17) (6,17) (18,11) (18,10) (4,7) (2,17) (5,7) (4,0) (12,8) (0,3) (17,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph74",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,4) (5,1) (8,6) (8,10) (3,4) (7,9) (2,7) (9,6) (3,0) (0,10) (10,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph306",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,11) (8,13) (12,10) (4,11) (10,8) (3,0) (9,2) (15,12) (9,6) (7,12) (5,9) (5,8) (13,14) (0,7) (1,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1398",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,5) (11,2) (17,8) (7,10) (14,17) (9,8) (4,16) (15,3) (13,3) (0,2) (5,18) (0,3) (15,5) (1,9) (12,9) (13,6) (0,1) (7,14) (14,16) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph606",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,15) (18,4) (4,14) (8,0) (17,19) (8,9) (15,2) (17,13) (1,12) (5,18) (10,11) (0,1) (6,15) (7,2) (20,3) (3,17) (11,18) (0,10) (13,6) (8,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph516",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,6) (0,10) (0,18) (4,12) (0,5) (5,16) (3,8) (15,8) (2,11) (18,12) (7,12) (6,1) (2,9) (13,6) (0,11) (9,17) (8,11) (0,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1544",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,0) (3,17) (3,5) (16,1) (20,14) (9,16) (19,11) (7,13) (4,8) (11,15) (3,18) (2,19) (14,0) (7,15) (7,12) (6,11) (20,8) (20,18) (17,12) (0,10) (5,1) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1151",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,13) (3,0) (2,4) (4,0) (0,5) (6,3) (14,4) (1,4) (5,11) (7,6) (4,8) (1,9) (10,4) (7,0) (12,1) (1,0) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1706",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (5,6) (23,4) (23,10) (8,12) (0,2) (0,1) (16,8) (5,12) (4,21) (12,1) (22,10) (0,20) (7,21) (18,11) (3,0) (9,17) (19,7) (3,7) (18,17) (12,23) (18,0) (14,4) (10,2) (9,15) (22,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1249",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,0) (10,11) (14,8) (7,14) (1,0) (6,13) (6,4) (3,10) (0,3) (4,3) (2,0) (2,15) (9,1) (12,2) (12,13) (9,4) (7,12) (5,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph612",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,13) (16,14) (19,12) (19,3) (2,13) (10,11) (18,1) (8,0) (10,8) (14,7) (8,15) (9,18) (5,2) (15,20) (17,6) (17,12) (11,4) (13,0) (0,3) (16,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph250",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,3) (14,6) (2,3) (13,3) (4,1) (11,6) (9,8) (2,12) (5,6) (3,7) (6,0) (11,4) (2,9) (12,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph92",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,7) (8,7) (8,1) (8,6) (7,11) (2,8) (9,10) (0,7) (3,9) (7,4) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph44",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,7) (8,0) (2,6) (9,3) (6,0) (3,10) (10,0) (4,7) (2,1) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph742",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,22) (8,10) (11,7) (3,5) (19,18) (17,14) (17,10) (13,11) (1,3) (0,21) (15,13) (14,4) (17,9) (1,6) (17,21) (14,18) (12,14) (20,16) (16,10) (4,13) (19,2) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph704",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,3) (4,6) (21,2) (16,19) (9,10) (4,1) (0,8) (21,20) (17,14) (17,5) (10,17) (12,8) (7,8) (11,0) (15,18) (2,12) (2,19) (15,16) (13,20) (3,6) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph69",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,2) (3,0) (11,10) (0,7) (10,0) (1,3) (0,4) (6,11) (8,5) (9,0) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph929",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,3) (10,1) (1,6) (7,4) (0,7) (2,0) (7,10) (4,5) (9,6) (8,1) (3,0) (7,2) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph684",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (4,9) (11,12) (13,2) (0,20) (2,20) (18,20) (8,10) (15,1) (19,7) (5,7) (7,15) (6,9) (10,17) (2,6) (8,11) (17,16) (18,21) (2,15) (8,14) (12,5) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph626",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,4) (13,11) (17,2) (9,6) (8,17) (19,8) (18,20) (5,7) (10,0) (3,10) (20,15) (0,16) (2,9) (11,17) (16,13) (5,14) (20,12) (7,8) (1,0) (2,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1222",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,15) (5,8) (13,8) (3,1) (6,0) (1,5) (3,0) (0,11) (13,4) (14,6) (1,15) (12,15) (10,14) (2,10) (2,0) (2,7) (15,7) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph486",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,9) (10,8) (2,16) (14,5) (12,7) (11,4) (10,16) (6,13) (10,14) (15,3) (3,0) (7,17) (4,3) (2,12) (12,13) (14,9) (4,6) (8,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph741",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (7,17) (22,13) (0,4) (6,21) (10,2) (16,13) (6,0) (11,3) (2,19) (8,20) (9,17) (18,0) (20,10) (16,14) (7,3) (20,12) (15,5) (11,19) (17,1) (18,8) (15,9) (22,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph973",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,11) (11,9) (11,4) (0,3) (0,1) (2,6) (2,4) (1,5) (8,3) (10,0) (3,7) (7,0) (1,3) (2,0) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph226",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,1) (12,6) (12,5) (0,2) (4,1) (12,7) (11,7) (9,4) (7,13) (1,7) (10,12) (9,2) (3,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1778",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (20,12) (18,11) (5,19) (6,17) (4,2) (9,15) (8,22) (3,13) (16,15) (5,16) (2,13) (0,1) (7,24) (0,21) (6,15) (1,5) (10,13) (0,22) (7,16) (4,24) (11,0) (7,23) (18,13) (20,16) (14,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph319",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,11) (9,6) (0,13) (9,7) (14,15) (8,11) (5,7) (4,0) (10,4) (8,14) (1,4) (1,6) (2,14) (1,3) (6,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph446",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,13) (1,5) (7,8) (9,14) (6,15) (6,16) (14,11) (17,12) (0,2) (14,5) (12,6) (2,5) (3,12) (11,15) (4,14) (14,10) (6,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph947",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,8) (5,2) (1,0) (9,7) (10,9) (4,10) (2,0) (5,4) (8,6) (1,9) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph811",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (19,23) (10,21) (13,14) (13,4) (20,8) (14,11) (10,19) (10,11) (23,7) (3,2) (1,19) (23,22) (11,2) (5,17) (21,16) (0,20) (18,11) (22,8) (15,1) (5,18) (9,3) (13,6) (12,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1175",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,0) (1,5) (6,12) (8,2) (9,7) (9,13) (6,14) (14,3) (8,0) (14,0) (5,13) (4,5) (0,2) (6,1) (3,10) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph686",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,12) (14,6) (1,4) (21,1) (8,18) (0,17) (11,1) (7,2) (14,15) (20,16) (5,1) (13,18) (0,6) (18,3) (8,20) (7,11) (15,10) (19,5) (13,9) (16,15) (10,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph835",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,20) (3,2) (20,12) (15,0) (1,7) (4,8) (0,19) (14,21) (14,6) (23,21) (13,0) (7,0) (17,15) (15,12) (5,9) (23,5) (18,10) (9,4) (22,11) (18,22) (17,9) (19,16) (10,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph539",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,10) (5,3) (7,14) (17,1) (17,18) (4,2) (15,5) (14,3) (9,14) (14,8) (4,9) (12,6) (16,13) (14,0) (2,17) (18,11) (15,16) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph98",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,2) (10,11) (11,4) (8,7) (0,1) (5,1) (2,1) (3,4) (9,5) (7,6) (2,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1291",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,11) (7,15) (2,0) (8,6) (0,1) (14,16) (3,9) (12,10) (1,12) (0,3) (9,6) (0,4) (0,5) (4,2) (8,1) (16,2) (12,14) (0,13) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph429",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,12) (8,4) (9,2) (4,11) (0,15) (6,16) (14,1) (1,12) (11,17) (1,13) (2,7) (1,2) (13,4) (9,5) (14,3) (15,6) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1299",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,2) (3,0) (15,16) (15,14) (16,1) (5,2) (3,10) (4,6) (10,13) (2,6) (1,10) (0,9) (8,7) (11,3) (12,16) (15,7) (0,1) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1110",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,8) (3,10) (13,1) (3,11) (0,2) (5,9) (3,9) (11,7) (2,7) (6,5) (4,0) (11,12) (3,0) (1,0) (1,2) (0,5) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph487",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,0) (10,3) (18,13) (6,15) (7,5) (12,15) (3,9) (5,11) (14,1) (0,17) (8,9) (8,13) (13,11) (4,12) (6,2) (1,4) (12,17) (6,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph711",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,8) (15,11) (16,14) (20,19) (4,12) (8,15) (15,1) (18,7) (9,11) (17,0) (16,5) (0,12) (0,21) (3,21) (21,19) (7,17) (14,19) (10,4) (11,13) (8,20) (21,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph82",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,3) (10,2) (8,0) (2,3) (5,6) (5,0) (4,9) (10,8) (7,0) (0,1) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph338",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,7) (4,14) (2,10) (8,9) (5,6) (0,14) (12,5) (4,13) (7,0) (1,12) (4,15) (12,8) (10,9) (3,7) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1399",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,0) (17,7) (9,2) (16,15) (13,9) (18,0) (8,4) (10,12) (5,11) (15,6) (1,5) (10,16) (14,15) (7,3) (18,13) (16,5) (8,16) (2,17) (0,2) (1,0) (9,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1084",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,10) (12,5) (10,3) (11,1) (5,13) (12,6) (10,13) (12,7) (2,4) (8,2) (0,11) (1,13) (0,1) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph399",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,11) (4,3) (11,12) (0,2) (2,6) (13,12) (8,2) (16,14) (10,16) (10,12) (9,5) (5,7) (12,15) (1,6) (9,4) (9,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1650",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,18) (5,1) (12,22) (22,19) (17,16) (20,11) (0,12) (0,11) (7,11) (0,2) (2,17) (9,21) (0,21) (4,18) (0,1) (1,20) (6,12) (13,8) (15,6) (1,10) (2,15) (14,9) (13,15) (3,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1442",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,5) (8,7) (9,6) (0,10) (17,11) (8,17) (18,2) (17,2) (2,0) (16,8) (18,13) (14,13) (12,5) (3,10) (1,0) (1,4) (19,13) (15,11) (0,16) (9,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph943",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,8) (6,2) (3,5) (2,0) (0,1) (1,5) (4,0) (2,4) (3,0) (0,7) (10,5) (8,9) (10,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph543",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,9) (14,19) (14,4) (19,9) (11,7) (6,17) (5,16) (0,10) (10,3) (15,12) (14,2) (17,8) (9,10) (0,15) (4,5) (17,0) (18,11) (16,1) (13,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1214",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,8) (7,3) (8,6) (4,13) (14,5) (0,1) (10,2) (15,3) (1,10) (2,9) (13,5) (0,3) (11,1) (5,0) (15,13) (2,0) (5,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph923",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,6) (0,6) (8,4) (7,4) (0,1) (2,6) (3,5) (4,10) (2,3) (9,8) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1323",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,8) (16,14) (6,11) (6,5) (15,0) (6,3) (9,15) (16,8) (17,12) (17,0) (13,7) (4,17) (10,7) (3,9) (0,2) (4,7) (0,1) (2,10) (8,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph529",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,9) (7,15) (2,4) (16,6) (10,1) (4,3) (13,5) (15,3) (4,5) (17,18) (7,6) (13,14) (9,16) (17,16) (0,17) (12,6) (17,10) (8,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1504",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (20,14) (5,14) (4,14) (19,11) (12,13) (0,3) (2,0) (19,9) (19,15) (8,16) (6,8) (5,1) (3,2) (7,13) (10,8) (1,17) (0,4) (1,0) (18,5) (1,9) (3,13) (15,13) (20,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph76",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,1) (4,7) (8,9) (10,3) (6,3) (3,5) (2,5) (8,7) (4,0) (11,9) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph464",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,11) (7,0) (16,10) (16,15) (8,12) (1,16) (5,3) (7,8) (7,5) (13,14) (12,17) (17,6) (10,11) (17,14) (17,2) (17,9) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1083",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,12) (11,12) (10,8) (9,7) (3,0) (8,6) (11,4) (1,0) (9,6) (0,10) (7,2) (0,2) (0,5) (4,0) (3,4) (1,5) (10,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph295",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,8) (1,6) (3,5) (10,2) (2,7) (14,6) (0,11) (11,12) (12,8) (5,14) (13,0) (0,9) (4,3) (13,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph813",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,11) (17,5) (14,13) (6,13) (9,3) (11,14) (0,20) (19,23) (22,8) (19,1) (5,18) (22,23) (11,18) (20,8) (13,4) (10,11) (21,10) (10,19) (12,22) (2,3) (1,15) (7,23) (21,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph694",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,6) (13,10) (4,3) (2,0) (12,18) (17,14) (20,21) (2,8) (16,19) (21,9) (9,4) (20,17) (15,11) (12,10) (5,7) (15,12) (12,16) (9,5) (17,13) (6,2) (2,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph362",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,8) (3,13) (13,11) (3,2) (14,2) (6,1) (14,4) (16,6) (14,7) (12,16) (0,4) (5,12) (11,10) (5,9) (8,14) (15,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1574",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,20) (9,18) (1,0) (13,8) (0,4) (2,18) (15,2) (0,8) (15,12) (9,19) (0,5) (2,0) (0,3) (17,5) (16,6) (14,3) (16,7) (1,8) (3,4) (16,12) (11,18) (6,14) (15,10) (14,5) (21,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1169",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,7) (0,6) (8,14) (3,7) (7,8) (13,6) (4,2) (4,1) (12,7) (5,13) (11,8) (4,8) (14,5) (0,1) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph805",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,22) (13,21) (15,21) (14,10) (23,16) (16,2) (10,3) (22,7) (19,21) (12,13) (12,20) (17,19) (0,3) (22,5) (9,14) (7,12) (8,14) (4,3) (1,9) (4,21) (6,18) (2,20) (11,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1053",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,3) (8,6) (0,9) (1,0) (0,10) (3,10) (2,0) (7,1) (0,3) (0,6) (5,7) (1,2) (12,2) (3,2) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph625",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,4) (5,11) (4,6) (0,19) (13,8) (19,16) (18,7) (0,10) (19,4) (3,16) (15,14) (9,12) (15,1) (8,2) (14,20) (8,20) (12,11) (17,7) (17,0) (15,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph510",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,13) (7,8) (0,3) (6,15) (3,17) (8,2) (2,18) (11,9) (4,8) (2,1) (1,9) (5,13) (16,9) (9,3) (0,15) (10,12) (14,15) (10,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph904",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,0) (6,9) (0,4) (5,0) (7,3) (1,9) (10,7) (0,6) (0,1) (9,7) (0,2) (3,0) (5,7) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph992",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,1) (4,1) (11,10) (8,3) (8,9) (8,11) (11,2) (7,1) (3,6) (5,10) (2,0) (5,4) (0,3) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1664",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,19) (1,0) (22,18) (21,10) (22,9) (15,21) (5,3) (11,9) (12,4) (0,3) (8,17) (7,12) (0,2) (14,11) (5,11) (19,2) (19,22) (1,2) (0,20) (7,10) (4,17) (16,19) (6,22) (0,22) (4,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph80",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,8) (6,4) (1,7) (4,9) (9,0) (6,10) (4,3) (5,8) (11,2) (1,0) (2,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1020",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,0) (11,4) (2,1) (9,8) (7,8) (1,0) (3,0) (11,8) (5,6) (3,6) (2,0) (6,2) (10,1) (12,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph256",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,9) (13,4) (13,12) (4,11) (0,1) (1,14) (1,8) (10,7) (7,4) (3,12) (14,6) (8,12) (5,6) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph89",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,1) (5,7) (3,11) (10,3) (4,7) (0,10) (9,3) (6,0) (0,8) (6,2) (1,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph143",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,1) (10,5) (9,3) (3,2) (1,10) (1,11) (10,12) (4,8) (7,0) (4,3) (0,11) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1603",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,10) (3,11) (1,0) (13,0) (21,8) (2,20) (7,8) (13,14) (4,10) (20,9) (14,18) (15,18) (5,17) (18,16) (5,0) (13,21) (6,4) (10,12) (2,3) (3,4) (1,21) (13,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1096",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (4,6) (0,3) (8,3) (4,7) (6,10) (9,0) (9,11) (9,12) (10,13) (5,8) (7,5) (0,1) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph862",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,8) (7,4) (0,7) (11,12) (14,23) (16,17) (1,16) (10,20) (7,5) (8,7) (24,12) (17,13) (9,12) (18,10) (17,22) (22,19) (6,17) (15,14) (2,17) (3,5) (18,21) (20,16) (21,11) (12,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1015",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,6) (4,3) (0,2) (10,1) (9,6) (2,7) (1,11) (0,3) (7,4) (7,0) (5,4) (0,1) (10,7) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1479",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,18) (0,2) (10,1) (18,13) (0,16) (11,7) (1,6) (2,3) (17,14) (18,8) (18,9) (3,0) (1,0) (1,15) (0,4) (5,12) (17,4) (10,2) (7,16) (19,17) (12,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph988",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,7) (2,0) (0,11) (6,8) (0,1) (9,2) (9,10) (3,6) (7,4) (10,7) (10,8) (7,1) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph333",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,8) (13,1) (11,4) (7,10) (2,5) (14,3) (2,13) (10,12) (3,0) (12,1) (14,6) (0,8) (12,11) (15,8) (13,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1161",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (3,12) (6,4) (1,12) (0,3) (0,2) (0,1) (8,6) (14,5) (2,14) (9,4) (13,11) (6,13) (14,10) (8,5) (0,4) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph55",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,9) (2,6) (7,5) (1,2) (0,8) (3,10) (7,1) (6,0) (10,0) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph48",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,2) (5,6) (8,4) (6,1) (7,3) (7,10) (6,7) (9,6) (1,0) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph28",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,5) (3,8) (7,10) (9,10) (2,4) (5,2) (0,3) (8,9) (7,6) (9,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1264",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,1) (10,15) (2,7) (5,10) (1,8) (7,4) (6,4) (0,3) (3,14) (14,0) (2,0) (5,12) (2,11) (8,7) (5,13) (13,1) (1,0) (0,9) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1600",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,10) (5,15) (20,12) (11,21) (8,11) (4,17) (8,12) (6,2) (7,5) (2,0) (11,14) (6,0) (8,19) (16,0) (9,16) (0,1) (10,14) (11,4) (3,7) (13,1) (1,21) (7,18) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph38",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,2) (1,3) (0,10) (6,0) (1,4) (7,10) (9,2) (6,4) (4,8) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph384",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,8) (13,8) (5,4) (11,8) (14,3) (12,1) (4,9) (16,1) (10,6) (9,13) (11,3) (7,4) (11,0) (15,16) (2,10) (0,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph203",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,13) (5,7) (8,2) (13,1) (3,8) (7,10) (13,6) (1,2) (12,0) (4,9) (4,6) (10,0) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph551",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,7) (1,12) (1,16) (0,18) (16,15) (14,16) (10,17) (2,6) (4,9) (8,7) (10,1) (2,5) (13,3) (0,19) (0,9) (11,19) (3,10) (15,11) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph938",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,3) (7,2) (9,5) (6,2) (2,0) (5,6) (10,1) (8,1) (7,4) (6,8) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph582",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,10) (11,12) (0,12) (18,6) (2,13) (11,5) (13,9) (16,4) (11,2) (18,16) (17,18) (10,3) (7,0) (4,3) (8,3) (0,14) (19,8) (7,15) (1,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph829",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,23) (5,3) (10,23) (14,0) (7,12) (20,13) (3,17) (20,1) (0,16) (16,19) (2,19) (18,3) (11,8) (15,11) (17,12) (23,6) (15,7) (8,4) (5,1) (7,14) (9,22) (20,21) (11,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph624",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (17,20) (13,15) (16,2) (17,1) (12,7) (14,17) (9,18) (10,8) (20,18) (5,17) (19,3) (11,16) (15,8) (3,1) (6,19) (4,3) (14,0) (11,5) (7,13) (14,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1712",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (16,20) (6,2) (3,10) (23,13) (2,5) (11,19) (10,21) (17,23) (11,15) (16,1) (0,17) (22,15) (1,0) (19,0) (6,4) (18,3) (4,9) (0,2) (3,0) (7,9) (16,22) (7,15) (1,10) (8,22) (14,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph292",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,3) (0,1) (5,10) (13,11) (5,14) (9,4) (9,7) (13,2) (2,1) (8,11) (2,4) (6,5) (1,12) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1562",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,16) (12,6) (20,15) (2,4) (5,13) (1,0) (9,16) (21,4) (10,1) (17,20) (21,16) (18,3) (11,9) (7,6) (17,10) (7,19) (6,16) (14,13) (4,5) (17,8) (17,0) (15,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1766",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (21,15) (9,5) (7,23) (6,0) (4,0) (13,5) (6,3) (22,23) (3,0) (24,15) (2,0) (22,9) (7,17) (15,13) (20,4) (22,18) (7,16) (2,4) (1,4) (14,5) (10,11) (2,11) (0,11) (1,0) (19,12) (23,3) (15,19) (14,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph298",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,12) (2,9) (8,6) (1,14) (2,11) (11,13) (6,10) (1,12) (6,5) (2,0) (7,12) (3,7) (7,4) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph308",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,15) (15,1) (6,8) (13,14) (12,3) (6,14) (3,5) (6,0) (8,10) (4,2) (6,9) (13,12) (7,0) (2,0) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph474",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,2) (2,1) (6,9) (3,8) (2,10) (9,10) (5,2) (5,14) (4,13) (7,17) (7,0) (11,12) (10,13) (4,8) (0,14) (16,6) (15,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1490",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (19,11) (15,19) (4,0) (18,9) (12,13) (1,0) (4,14) (1,9) (13,7) (13,3) (8,10) (14,5) (3,2) (13,15) (19,14) (6,1) (1,5) (0,5) (5,17) (8,16) (0,3) (2,0) (6,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph3",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (0,2) (6,7) (9,0) (8,1) (2,5) (3,8) (8,2) (8,4) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph59",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,10) (5,6) (7,5) (2,8) (3,6) (6,8) (9,8) (1,6) (5,4) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1546",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,8) (13,20) (3,9) (6,15) (7,0) (13,11) (17,0) (0,1) (2,6) (5,7) (9,8) (20,4) (1,20) (12,15) (19,6) (14,1) (16,4) (18,12) (10,3) (11,5) (0,2) (17,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph332",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,3) (6,3) (10,15) (5,9) (10,6) (8,12) (2,12) (15,7) (9,1) (1,8) (0,4) (11,1) (13,9) (6,0) (3,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1790",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (13,4) (18,5) (8,4) (15,22) (12,19) (14,5) (1,0) (14,19) (23,6) (24,7) (1,2) (9,22) (18,2) (4,20) (2,10) (21,22) (2,11) (19,0) (13,10) (2,0) (3,24) (10,21) (7,0) (17,11) (9,6) (16,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1324",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,2) (7,8) (0,10) (8,4) (0,3) (6,11) (13,14) (5,12) (2,0) (11,16) (1,0) (2,10) (12,1) (14,3) (17,14) (9,0) (10,17) (14,5) (16,1) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1090",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,3) (0,9) (6,13) (0,6) (6,5) (10,3) (5,1) (4,11) (0,2) (3,7) (8,4) (7,2) (1,0) (12,4) (4,0) (3,0) (13,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph603",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,20) (11,6) (0,11) (1,0) (18,12) (0,13) (2,20) (17,16) (18,8) (17,1) (14,19) (15,14) (0,2) (1,9) (15,3) (7,10) (3,10) (4,6) (8,11) (5,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph977",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (3,6) (9,10) (5,11) (7,8) (1,0) (0,11) (2,0) (11,6) (11,4) (1,8) (1,9) (2,7) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph400",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,0) (11,10) (2,16) (10,5) (3,0) (14,9) (3,4) (12,15) (11,7) (13,14) (7,6) (8,6) (13,3) (7,14) (6,1) (12,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1120",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (4,0) (5,0) (1,0) (10,12) (1,9) (3,10) (0,3) (5,8) (12,11) (13,12) (5,9) (6,12) (1,2) (7,2) (13,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph826",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,11) (14,6) (2,19) (5,19) (15,10) (16,23) (3,6) (23,5) (7,16) (4,8) (23,14) (21,4) (8,23) (18,0) (0,1) (14,17) (23,11) (1,5) (22,1) (12,22) (16,13) (11,20) (22,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1421",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,15) (6,0) (9,0) (2,0) (0,1) (0,3) (2,4) (3,5) (18,0) (16,13) (7,17) (8,11) (17,2) (12,0) (4,15) (13,14) (6,14) (12,2) (10,6) (3,12) (6,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1582",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,5) (9,3) (10,7) (9,15) (14,7) (4,7) (4,17) (12,17) (1,8) (0,1) (15,0) (19,16) (21,15) (6,11) (2,10) (0,16) (8,20) (0,2) (13,19) (6,3) (0,8) (20,17) (21,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1564",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (19,8) (0,6) (20,10) (1,0) (15,5) (21,18) (0,3) (6,20) (2,17) (1,17) (12,20) (8,18) (14,16) (13,16) (0,2) (7,13) (10,2) (9,15) (3,7) (18,0) (19,11) (9,17) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph259",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,1) (10,5) (3,9) (11,0) (1,12) (14,11) (8,4) (13,14) (2,11) (7,0) (2,3) (6,1) (4,3) (11,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1453",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,11) (8,15) (2,12) (0,3) (10,9) (4,2) (7,10) (6,7) (0,15) (4,11) (10,14) (2,0) (17,13) (8,1) (19,7) (2,17) (5,11) (3,11) (15,7) (3,18) (0,1) (4,0) (16,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph690",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,3) (13,0) (15,14) (1,9) (11,8) (13,5) (18,12) (17,1) (18,8) (11,6) (14,19) (0,1) (0,2) (4,6) (2,20) (21,15) (7,21) (10,7) (10,3) (11,0) (16,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1238",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,13) (3,0) (0,5) (1,11) (12,5) (15,3) (3,7) (0,2) (5,13) (10,1) (15,13) (8,5) (1,0) (8,6) (2,9) (10,2) (5,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1768",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,21) (21,15) (6,17) (7,14) (4,16) (1,0) (2,22) (4,5) (9,3) (19,23) (8,21) (23,9) (13,4) (20,5) (0,13) (21,10) (1,8) (18,7) (11,5) (9,0) (12,20) (2,17) (7,20) (21,24) (6,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1236",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,0) (10,9) (14,0) (7,14) (4,8) (12,4) (11,3) (7,13) (7,10) (6,9) (5,11) (15,0) (11,12) (0,3) (1,0) (2,5) (0,4) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1257",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,10) (0,8) (13,1) (0,3) (2,0) (6,14) (0,1) (14,3) (12,11) (13,2) (13,0) (0,4) (11,4) (2,5) (10,12) (8,15) (12,1) (9,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph649",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,14) (11,18) (10,16) (14,9) (2,4) (9,4) (15,20) (8,14) (5,19) (17,20) (1,17) (13,16) (14,0) (3,14) (6,5) (3,5) (12,6) (15,16) (18,19) (17,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph590",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,17) (4,12) (19,8) (1,2) (5,3) (16,10) (7,10) (17,12) (5,11) (11,9) (0,19) (14,0) (11,13) (19,2) (9,19) (7,18) (4,15) (7,14) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1305",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,0) (1,0) (16,5) (11,7) (9,15) (8,3) (13,11) (12,13) (0,4) (9,1) (0,10) (0,16) (4,14) (14,13) (2,1) (6,4) (5,12) (3,14) (2,0) (11,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1212",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,2) (13,9) (6,8) (15,1) (10,8) (15,5) (0,14) (12,9) (0,4) (13,7) (11,3) (1,6) (2,11) (3,7) (2,0) (1,0) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph601",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,17) (1,12) (4,12) (5,4) (14,10) (20,13) (6,9) (1,7) (13,0) (18,2) (0,19) (8,7) (8,16) (18,9) (4,11) (20,7) (1,10) (14,15) (2,5) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1521",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,5) (9,13) (2,0) (11,14) (8,11) (13,16) (1,10) (4,15) (20,14) (13,5) (14,12) (19,0) (1,17) (15,7) (1,3) (18,20) (16,6) (1,0) (12,17) (5,4) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph844",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,16) (15,2) (20,7) (7,0) (12,14) (10,9) (8,7) (9,22) (15,13) (18,20) (4,21) (3,15) (0,9) (19,24) (0,14) (5,9) (13,21) (17,8) (6,13) (10,21) (1,11) (4,23) (23,19) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1099",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,0) (13,10) (9,11) (13,6) (2,12) (1,0) (0,4) (8,1) (10,9) (7,9) (12,3) (4,5) (0,6) (4,3) (8,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1050",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,6) (10,12) (8,5) (4,0) (4,8) (3,8) (10,11) (0,6) (2,0) (2,9) (12,4) (0,3) (1,0) (9,7) (8,1) (9,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph576",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,0) (8,18) (15,13) (1,17) (11,3) (15,5) (19,11) (16,2) (0,4) (10,2) (14,9) (6,0) (12,16) (10,8) (7,3) (17,9) (17,6) (19,18) (7,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1587",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,13) (0,15) (1,20) (1,4) (0,3) (0,1) (4,8) (1,18) (21,19) (1,10) (4,15) (7,17) (14,17) (0,2) (4,11) (3,12) (12,6) (3,17) (7,4) (21,9) (4,16) (14,21) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1193",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,14) (1,0) (13,8) (5,14) (4,13) (3,0) (0,9) (11,3) (13,6) (12,13) (2,12) (0,2) (1,6) (0,14) (7,10) (0,7) (10,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph858",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,15) (18,4) (24,6) (3,5) (21,1) (23,20) (3,13) (21,23) (4,9) (2,0) (8,12) (4,12) (4,19) (11,1) (1,4) (22,1) (0,15) (7,17) (7,4) (21,10) (7,14) (16,24) (17,24) (3,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph903",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,10) (6,9) (1,4) (2,4) (3,4) (8,2) (0,2) (0,4) (1,0) (3,0) (9,7) (7,3) (7,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1352",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (1,8) (0,2) (12,1) (0,5) (7,16) (12,11) (3,17) (4,0) (14,13) (1,0) (7,0) (12,4) (2,4) (9,0) (8,6) (16,15) (10,6) (9,5) (2,17) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1028",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,6) (7,5) (3,0) (5,10) (1,0) (0,2) (8,10) (7,1) (6,0) (3,4) (0,5) (2,11) (10,4) (9,8) (0,4) (12,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1474",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,17) (6,12) (6,1) (13,10) (16,12) (9,12) (4,0) (17,15) (18,10) (19,14) (15,1) (0,1) (17,3) (18,6) (14,2) (15,5) (14,7) (8,15) (9,4) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1029",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,9) (11,10) (4,2) (5,4) (5,12) (8,0) (9,11) (3,11) (11,6) (10,8) (1,0) (7,12) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph293",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,2) (9,13) (1,4) (6,3) (0,1) (11,2) (12,11) (11,7) (8,4) (10,1) (3,2) (14,5) (1,5) (13,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph871",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,17) (16,7) (12,15) (13,8) (0,13) (14,5) (0,3) (1,8) (14,3) (24,13) (3,4) (21,8) (22,24) (14,6) (9,18) (2,18) (23,0) (6,16) (12,16) (15,10) (16,20) (19,9) (15,2) (18,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph527",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,6) (4,0) (14,9) (5,16) (12,17) (15,10) (12,13) (1,2) (0,15) (8,10) (11,1) (5,0) (18,12) (16,7) (18,3) (16,11) (11,12) (13,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1287",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,13) (8,13) (0,2) (16,5) (9,15) (6,1) (6,8) (1,0) (3,2) (13,11) (8,10) (3,13) (14,4) (1,5) (5,14) (15,12) (1,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph390",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,16) (0,3) (0,10) (9,8) (8,1) (2,15) (6,8) (5,15) (3,15) (3,9) (0,13) (9,14) (12,2) (4,13) (2,7) (10,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1297",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,14) (0,2) (15,12) (13,4) (8,5) (10,2) (15,10) (5,1) (3,1) (9,15) (0,1) (6,0) (0,11) (2,7) (13,8) (16,1) (14,15) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1131",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,0) (10,13) (7,11) (9,1) (0,3) (12,4) (6,5) (7,3) (4,0) (8,9) (7,13) (6,7) (13,4) (2,0) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1513",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,14) (0,16) (7,3) (1,2) (14,3) (0,14) (11,18) (13,17) (9,1) (15,9) (18,16) (8,19) (13,12) (19,11) (5,4) (0,1) (19,10) (11,6) (12,20) (2,0) (19,17) (0,3) (13,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph964",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,3) (7,1) (5,7) (6,2) (3,10) (4,7) (1,0) (2,1) (0,6) (9,3) (0,10) (0,8) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph373",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,7) (10,14) (4,9) (1,11) (13,5) (9,16) (3,15) (8,7) (7,6) (2,15) (8,13) (9,0) (14,7) (11,0) (12,13) (9,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph291",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,12) (4,1) (10,3) (13,8) (2,11) (10,4) (4,0) (10,2) (9,14) (13,3) (14,5) (6,10) (10,12) (14,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1655",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,14) (1,0) (19,5) (0,5) (15,9) (3,1) (6,20) (21,3) (7,12) (6,8) (16,22) (15,18) (17,20) (2,0) (5,15) (6,7) (9,14) (13,15) (3,10) (10,11) (21,2) (10,16) (8,22) (8,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph748",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (16,5) (2,21) (19,15) (17,16) (1,21) (10,17) (22,21) (12,4) (9,19) (11,1) (7,19) (22,13) (1,14) (13,18) (6,3) (22,6) (6,20) (8,13) (15,4) (20,5) (6,0) (7,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph272",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,11) (3,5) (11,4) (12,4) (2,13) (14,0) (14,6) (8,10) (0,13) (9,11) (1,4) (10,13) (1,3) (7,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1198",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,2) (9,6) (4,14) (11,10) (11,4) (5,1) (12,3) (6,13) (0,1) (7,0) (13,10) (7,5) (8,4) (7,3) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph568",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,9) (12,4) (0,2) (14,0) (1,8) (14,17) (7,0) (8,6) (4,2) (3,17) (13,6) (15,12) (1,12) (19,9) (19,2) (16,18) (0,10) (16,7) (19,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1063",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,5) (8,3) (6,1) (6,12) (4,5) (8,4) (5,0) (7,10) (6,8) (2,1) (7,9) (6,11) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1426",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (10,3) (9,15) (15,16) (8,15) (8,2) (6,14) (13,3) (11,12) (13,5) (11,17) (1,7) (11,15) (0,1) (14,0) (4,18) (10,2) (8,14) (18,8) (1,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1386",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (4,17) (9,8) (15,16) (4,18) (0,2) (15,3) (2,11) (18,5) (2,1) (14,9) (17,2) (13,18) (6,0) (10,11) (8,15) (7,9) (3,0) (1,0) (12,14) (6,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph726",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,2) (18,13) (4,21) (9,17) (9,16) (0,20) (5,6) (21,7) (4,14) (0,14) (7,19) (4,10) (12,18) (3,7) (17,8) (22,5) (15,22) (18,0) (10,5) (12,8) (1,12) (12,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1696",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (2,18) (21,11) (12,21) (1,20) (3,14) (12,5) (19,22) (15,16) (14,19) (10,0) (8,9) (23,22) (4,8) (10,2) (19,17) (22,5) (7,11) (0,1) (2,0) (1,23) (10,17) (3,0) (6,19) (5,4) (14,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph109",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,6) (4,11) (2,1) (3,10) (3,2) (3,9) (4,1) (9,7) (0,6) (2,8) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph583",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,18) (8,19) (4,10) (3,2) (8,10) (14,15) (14,3) (16,17) (9,12) (11,3) (16,8) (10,5) (5,14) (16,1) (6,13) (7,3) (6,11) (9,5) (0,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph976",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (9,4) (4,0) (8,4) (0,1) (2,0) (8,7) (11,3) (0,7) (5,10) (8,6) (11,6) (3,10) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1687",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,1) (13,23) (0,2) (5,19) (14,15) (7,8) (4,21) (12,4) (5,22) (4,0) (3,9) (10,14) (13,0) (17,15) (7,20) (9,6) (23,5) (20,0) (1,10) (2,18) (1,7) (18,9) (21,2) (0,1) (0,3) (16,8) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1716",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,9) (8,16) (4,20) (20,21) (7,19) (13,2) (2,4) (0,2) (3,5) (0,22) (17,20) (6,15) (0,1) (0,23) (22,19) (6,14) (13,14) (1,15) (3,20) (18,6) (23,6) (21,11) (17,10) (8,22) (0,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph305",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,5) (10,12) (6,7) (0,10) (6,14) (8,4) (13,11) (8,14) (4,11) (1,3) (2,9) (9,15) (12,14) (15,1) (15,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1330",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,1) (6,11) (11,16) (3,0) (8,2) (2,11) (4,5) (14,5) (0,1) (17,3) (3,7) (4,0) (4,9) (11,12) (3,13) (0,15) (15,3) (2,0) (10,12) (3,12) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1303",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,2) (10,6) (15,6) (0,3) (13,4) (9,13) (6,16) (4,6) (7,3) (4,7) (4,1) (5,12) (4,5) (14,8) (12,14) (11,6) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph391",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,11) (1,15) (14,0) (3,4) (10,8) (9,15) (6,7) (15,3) (12,8) (3,16) (10,14) (2,16) (5,3) (7,13) (1,14) (11,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1251",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (11,14) (7,8) (4,8) (12,1) (2,10) (6,11) (14,3) (1,10) (0,10) (5,14) (13,2) (5,12) (4,5) (9,0) (15,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1750",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,18) (7,2) (16,20) (6,19) (20,22) (8,4) (1,13) (11,4) (0,1) (14,3) (0,15) (15,6) (2,0) (23,2) (9,5) (11,9) (22,24) (14,1) (1,2) (17,6) (1,12) (5,21) (9,17) (4,13) (15,20) (12,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph836",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,4) (15,19) (14,19) (13,12) (11,19) (9,22) (4,14) (5,22) (19,17) (12,23) (13,16) (3,10) (21,8) (2,1) (3,14) (18,11) (20,15) (0,21) (7,11) (16,0) (1,9) (22,18) (13,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph868",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,2) (5,6) (7,14) (14,8) (20,17) (3,4) (18,24) (13,11) (1,22) (23,19) (7,6) (0,6) (10,3) (24,9) (21,22) (21,18) (24,7) (7,17) (24,10) (15,21) (12,17) (11,18) (16,12) (18,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph61",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (8,5) (11,7) (7,2) (9,11) (10,5) (1,10) (7,1) (2,6) (4,0) (11,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph821",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (2,19) (21,6) (17,7) (8,18) (10,20) (13,22) (19,11) (10,2) (7,3) (6,23) (3,11) (18,0) (15,9) (14,16) (6,18) (17,9) (17,1) (4,0) (13,16) (8,20) (15,5) (20,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph34",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,1) (0,7) (2,6) (10,2) (8,9) (0,5) (3,5) (10,5) (0,8) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1349",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,12) (11,3) (9,10) (2,0) (0,14) (3,15) (0,1) (3,0) (13,14) (10,5) (17,6) (4,17) (3,13) (16,12) (16,2) (7,0) (16,6) (0,6) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1685",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,17) (21,16) (15,11) (1,0) (8,15) (23,18) (14,2) (16,5) (17,9) (16,19) (0,2) (3,0) (8,6) (20,22) (19,0) (20,6) (4,13) (18,1) (12,0) (17,3) (7,23) (0,4) (20,23) (20,2) (6,19) (10,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1530",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (17,18) (10,0) (3,4) (18,13) (6,2) (13,1) (7,8) (16,19) (12,7) (4,14) (20,19) (16,7) (8,11) (0,2) (6,7) (5,20) (3,0) (0,1) (9,3) (2,15) (3,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1103",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,13) (2,11) (10,12) (0,3) (1,8) (4,9) (5,1) (0,1) (6,13) (3,5) (0,2) (7,12) (3,9) (13,11) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph381",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,0) (7,5) (1,9) (11,16) (2,14) (2,7) (7,13) (6,14) (10,13) (14,12) (15,10) (9,3) (8,16) (9,14) (14,8) (16,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1279",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,3) (2,11) (11,3) (0,1) (2,7) (4,6) (0,2) (5,12) (4,7) (13,5) (10,5) (1,16) (1,13) (7,8) (10,15) (0,9) (0,14) (1,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph406",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,6) (12,5) (13,9) (1,3) (15,11) (3,10) (2,14) (15,5) (16,8) (4,7) (10,15) (5,0) (8,14) (6,15) (6,7) (14,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1147",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,3) (9,8) (11,4) (0,1) (2,3) (7,3) (12,2) (0,2) (5,6) (11,6) (6,0) (4,1) (14,6) (2,9) (12,1) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1573",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (14,18) (0,1) (17,19) (18,11) (21,17) (4,21) (13,17) (2,15) (9,1) (8,0) (2,5) (11,10) (18,3) (15,6) (0,2) (6,13) (16,15) (12,4) (10,0) (8,15) (3,0) (21,20) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph197",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,11) (13,7) (13,12) (4,2) (0,8) (12,5) (6,11) (11,3) (10,11) (8,10) (9,1) (5,4) (0,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1237",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,2) (15,6) (10,0) (3,15) (12,7) (0,3) (1,4) (15,4) (0,4) (2,9) (5,4) (7,6) (8,6) (6,14) (10,5) (9,13) (4,13) (1,0) (3,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1293",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,9) (0,2) (1,0) (13,15) (12,16) (3,0) (14,13) (2,12) (5,3) (4,2) (4,11) (3,12) (14,6) (0,6) (8,10) (0,7) (8,6) (1,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph503",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,13) (14,4) (1,2) (5,18) (12,5) (17,13) (3,14) (3,8) (14,13) (11,16) (15,18) (4,6) (16,0) (9,15) (10,0) (1,9) (11,7) (11,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph955",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,8) (8,3) (4,2) (9,1) (7,10) (1,0) (3,0) (9,10) (2,0) (5,2) (5,9) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph419",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,4) (1,2) (14,16) (4,12) (15,0) (14,7) (4,0) (11,12) (13,7) (11,5) (14,0) (7,10) (3,11) (2,5) (6,9) (9,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1070",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,4) (7,10) (5,12) (12,3) (2,0) (4,8) (1,6) (12,7) (7,1) (0,1) (9,2) (9,12) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1023",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (2,6) (0,6) (8,11) (5,1) (4,0) (5,3) (0,3) (2,0) (8,4) (6,12) (2,3) (9,11) (4,6) (9,7) (10,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1660",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,4) (9,15) (5,9) (18,10) (14,19) (14,7) (12,6) (1,15) (15,17) (3,14) (0,5) (2,19) (12,18) (0,4) (6,1) (17,2) (13,7) (12,11) (6,20) (21,14) (22,17) (0,3) (10,16) (15,8) (2,0) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1365",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,16) (8,2) (15,2) (14,0) (0,4) (0,10) (10,12) (11,9) (3,9) (1,17) (15,9) (0,3) (4,8) (1,0) (0,5) (6,15) (7,8) (13,2) (1,9) (0,2) (13,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1336",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (3,0) (17,11) (4,12) (0,7) (4,1) (9,8) (13,8) (15,6) (0,1) (14,6) (13,1) (3,10) (2,6) (5,11) (16,0) (17,12) (3,9) (15,12) (7,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1392",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (6,17) (11,9) (11,8) (7,16) (18,2) (2,0) (17,0) (11,5) (12,15) (9,4) (2,14) (3,5) (0,1) (0,14) (1,2) (14,7) (7,10) (4,12) (4,0) (13,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1575",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,0) (19,16) (0,1) (4,0) (20,17) (12,17) (1,8) (7,10) (0,3) (15,9) (10,2) (21,18) (4,7) (21,15) (11,6) (8,0) (17,4) (5,6) (13,19) (0,2) (0,15) (3,6) (20,8) (3,9) (7,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1472",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,1) (13,3) (1,10) (18,14) (19,18) (16,6) (1,8) (17,6) (12,2) (0,6) (2,0) (3,18) (11,8) (16,19) (0,3) (1,0) (0,4) (15,7) (9,18) (15,3) (13,12) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph564",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,9) (11,18) (4,5) (1,14) (19,7) (13,18) (4,12) (2,13) (1,6) (11,3) (17,13) (2,1) (7,2) (10,0) (12,3) (17,10) (6,16) (8,1) (15,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1270",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,12) (0,7) (8,6) (0,3) (0,15) (2,3) (4,6) (14,8) (1,9) (0,4) (16,12) (14,16) (7,14) (9,5) (13,11) (4,11) (13,9) (0,2) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph922",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,10) (1,5) (9,8) (5,3) (7,4) (9,6) (8,4) (6,2) (3,2) (0,4) (0,1) (2,0) (3,0) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph501",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,3) (3,1) (3,11) (8,16) (16,0) (11,6) (9,7) (13,14) (2,10) (5,10) (16,15) (9,5) (10,8) (12,6) (3,4) (8,18) (14,5) (17,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1742",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (9,18) (8,16) (23,5) (18,2) (20,0) (14,15) (3,0) (1,10) (5,4) (23,13) (12,22) (15,17) (4,24) (21,4) (8,7) (1,12) (9,6) (0,1) (7,20) (7,1) (10,14) (3,9) (11,4) (5,19) (13,0) (21,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1163",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,0) (9,3) (5,2) (9,0) (13,1) (8,2) (9,10) (4,3) (10,7) (8,6) (9,11) (9,1) (1,0) (7,12) (14,5) (0,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph260",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,14) (1,12) (0,2) (8,3) (8,12) (13,10) (5,11) (6,8) (4,8) (11,2) (12,2) (13,7) (7,0) (14,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1123",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (4,0) (11,7) (5,0) (0,1) (10,13) (7,3) (6,0) (7,6) (13,4) (9,1) (9,0) (0,3) (8,9) (6,5) (7,13) (4,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph192",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,1) (3,6) (4,5) (6,8) (11,12) (2,5) (3,1) (0,10) (13,0) (11,0) (9,5) (10,7) (12,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1632",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,13) (1,0) (2,7) (1,2) (5,9) (4,13) (2,21) (0,2) (8,4) (6,19) (6,17) (15,6) (12,1) (6,18) (20,5) (16,20) (12,10) (14,3) (1,14) (11,9) (17,9) (15,22) (15,0) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph738",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,12) (15,1) (9,15) (17,4) (14,3) (12,6) (21,14) (7,13) (9,5) (4,0) (17,15) (20,6) (1,6) (22,17) (10,16) (7,14) (14,19) (19,2) (12,18) (10,18) (15,8) (2,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1623",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (18,20) (19,16) (1,13) (2,0) (0,1) (10,0) (4,3) (7,6) (6,2) (17,15) (8,7) (22,0) (5,20) (3,21) (19,0) (18,13) (8,11) (9,3) (4,14) (2,17) (21,2) (3,0) (12,7) (7,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1335",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (6,1) (6,2) (11,2) (5,9) (12,14) (17,10) (8,2) (2,0) (7,5) (4,3) (17,11) (0,3) (15,9) (12,10) (13,12) (16,15) (12,16) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph418",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,7) (0,15) (7,3) (0,2) (4,12) (3,11) (4,8) (4,1) (16,7) (10,4) (9,1) (1,15) (12,6) (1,14) (5,3) (13,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph776",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,21) (7,21) (11,14) (19,5) (9,19) (15,1) (13,14) (4,14) (21,0) (18,16) (20,8) (21,19) (12,9) (14,20) (6,2) (17,11) (13,12) (16,3) (16,10) (22,4) (2,19) (1,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph112",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,10) (2,6) (2,10) (10,4) (9,10) (3,2) (4,0) (8,3) (4,1) (10,5) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph310",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,3) (10,11) (12,10) (14,2) (14,15) (4,15) (6,12) (5,15) (14,7) (6,1) (7,9) (0,4) (1,15) (6,13) (12,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1191",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,12) (2,0) (2,10) (4,6) (13,10) (8,3) (6,9) (11,14) (2,7) (0,11) (2,3) (2,9) (1,10) (1,0) (13,5) (11,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1233",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,6) (1,0) (9,11) (5,7) (10,5) (4,2) (8,14) (0,6) (15,3) (14,15) (11,2) (7,15) (13,4) (1,4) (12,7) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph54",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (8,2) (9,0) (9,6) (10,2) (3,10) (9,8) (0,5) (1,4) (3,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph280",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,12) (7,1) (7,14) (13,11) (3,6) (12,10) (13,7) (0,5) (8,9) (0,11) (9,2) (8,10) (14,10) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph350",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,2) (4,10) (6,13) (8,13) (13,14) (1,5) (13,5) (4,15) (6,0) (15,7) (12,7) (1,11) (9,1) (7,0) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph925",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (4,1) (7,3) (8,3) (3,6) (4,0) (5,0) (5,9) (1,5) (3,0) (7,5) (0,2) (0,1) (9,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph672",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,7) (16,14) (15,11) (3,21) (6,12) (20,6) (6,7) (4,21) (18,1) (13,14) (2,0) (12,5) (5,9) (5,2) (19,18) (14,17) (14,8) (19,11) (10,14) (6,15) (12,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph58",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,2) (5,4) (1,7) (8,3) (0,7) (6,2) (5,0) (3,5) (7,10) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph376",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,8) (0,12) (14,16) (7,3) (15,7) (5,14) (6,10) (11,16) (13,4) (12,1) (5,4) (14,10) (3,4) (2,6) (0,10) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1558",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,1) (7,0) (4,2) (0,20) (19,9) (0,14) (1,12) (18,4) (19,16) (11,19) (12,17) (16,7) (1,8) (2,14) (8,6) (12,20) (6,15) (20,13) (0,10) (9,5) (3,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1704",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,0) (0,2) (17,18) (10,3) (9,7) (11,0) (9,23) (0,5) (3,21) (8,22) (1,0) (20,14) (13,18) (2,20) (14,15) (19,23) (16,0) (0,4) (11,8) (17,1) (11,6) (5,13) (12,1) (21,15) (4,6) (10,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1075",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,6) (10,1) (1,2) (6,2) (3,6) (3,12) (4,0) (11,4) (1,0) (0,3) (2,0) (11,8) (8,9) (7,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1410",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,2) (15,1) (6,16) (1,0) (13,10) (17,3) (17,18) (14,7) (18,10) (9,4) (8,15) (5,15) (17,15) (6,12) (12,14) (4,0) (1,6) (11,7) (12,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph995",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,5) (3,10) (3,0) (1,0) (2,7) (6,8) (2,1) (0,4) (9,5) (11,6) (5,0) (8,5) (1,9) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph786",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,10) (20,12) (3,16) (3,12) (23,15) (18,0) (22,6) (23,9) (6,23) (23,7) (0,8) (13,3) (5,10) (14,0) (0,1) (18,6) (2,22) (20,17) (14,13) (21,16) (4,17) (16,11) (9,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph281",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,12) (9,12) (11,14) (9,7) (12,4) (8,4) (9,2) (10,13) (8,3) (5,8) (1,8) (10,12) (6,0) (6,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph560",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,0) (2,12) (4,16) (13,14) (2,4) (12,7) (17,9) (8,6) (15,8) (10,0) (2,18) (12,0) (11,6) (5,3) (13,17) (3,19) (14,6) (19,0) (1,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1683",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (10,5) (11,6) (20,8) (8,10) (12,3) (3,11) (3,14) (4,3) (13,9) (18,16) (14,17) (7,10) (9,5) (0,22) (19,1) (0,1) (16,8) (2,0) (16,19) (0,19) (22,23) (15,6) (14,5) (2,16) (21,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph956",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,0) (0,5) (6,1) (2,10) (0,2) (0,1) (10,5) (8,0) (9,8) (0,7) (4,3) (5,3) (2,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1277",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,10) (16,0) (5,7) (8,15) (6,8) (12,11) (3,5) (0,1) (12,0) (12,7) (16,13) (4,7) (14,9) (14,10) (2,16) (8,12) (7,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph216",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,6) (1,7) (11,13) (5,0) (10,7) (10,8) (4,7) (8,9) (10,12) (0,11) (12,6) (9,2) (13,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1634",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,1) (14,18) (15,12) (10,3) (22,14) (2,19) (7,11) (11,9) (5,6) (19,18) (21,13) (10,18) (19,21) (8,14) (7,21) (6,0) (17,7) (12,17) (3,4) (0,1) (6,7) (16,17) (18,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1698",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,0) (23,10) (5,9) (15,17) (3,0) (21,16) (0,2) (8,23) (23,11) (6,9) (9,2) (7,2) (10,12) (13,23) (12,17) (23,4) (19,15) (22,13) (11,2) (6,1) (14,5) (12,20) (16,12) (21,18) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1205",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,7) (6,10) (9,13) (15,6) (1,0) (4,6) (14,12) (7,4) (4,1) (8,14) (5,2) (0,2) (6,11) (3,0) (4,0) (12,5) (4,13) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph752",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,21) (11,3) (12,15) (19,21) (7,10) (1,8) (7,22) (2,14) (10,16) (10,13) (17,2) (9,22) (20,17) (4,2) (11,10) (20,6) (7,18) (7,8) (17,15) (0,15) (4,11) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1295",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,0) (0,15) (2,1) (2,9) (15,6) (13,4) (12,10) (5,6) (1,12) (16,4) (3,14) (13,1) (11,1) (5,9) (7,2) (8,4) (14,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph243",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,1) (7,10) (11,7) (13,0) (2,4) (0,14) (4,3) (12,5) (9,2) (9,8) (14,5) (7,14) (3,12) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph505",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,17) (12,2) (5,10) (10,9) (15,11) (10,18) (6,7) (11,2) (4,17) (15,1) (0,15) (13,0) (8,9) (14,12) (16,11) (10,14) (3,5) (6,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph265",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,7) (9,0) (7,10) (5,14) (9,1) (8,2) (3,9) (9,11) (5,2) (0,14) (9,10) (6,8) (1,13) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph808",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (13,20) (23,12) (7,5) (1,18) (13,5) (22,16) (21,18) (5,21) (9,15) (11,2) (11,16) (8,9) (11,23) (20,12) (0,1) (8,19) (19,6) (23,10) (21,14) (3,2) (4,2) (1,19) (17,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1009",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,1) (7,0) (2,0) (0,1) (0,5) (8,2) (6,11) (4,0) (0,3) (3,2) (11,10) (9,0) (8,5) (10,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph402",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,5) (4,16) (15,10) (1,9) (14,6) (14,8) (16,11) (14,12) (9,14) (2,7) (7,13) (13,0) (2,14) (9,3) (8,16) (10,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph899",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,13) (8,9) (16,4) (23,13) (19,14) (23,3) (2,20) (9,1) (17,8) (15,18) (2,0) (17,3) (22,2) (4,22) (21,11) (23,24) (5,22) (14,7) (23,11) (9,12) (10,7) (15,5) (14,16) (5,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1376",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,2) (8,11) (9,2) (15,7) (7,16) (11,12) (2,6) (15,0) (12,5) (1,8) (8,10) (7,5) (10,14) (0,1) (3,9) (17,15) (13,17) (0,2) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph110",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,10) (1,2) (8,5) (6,11) (0,4) (10,3) (9,5) (1,0) (6,8) (9,1) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph130",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,11) (7,2) (11,5) (8,1) (11,0) (4,11) (6,7) (7,12) (8,10) (9,1) (9,3) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph457",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,0) (5,1) (12,10) (11,6) (11,2) (15,3) (11,12) (4,5) (3,12) (16,11) (3,17) (1,17) (9,4) (14,5) (13,3) (7,3) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1555",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (9,5) (15,3) (14,0) (10,9) (10,4) (11,1) (14,12) (20,16) (15,13) (19,20) (18,9) (8,13) (4,0) (15,2) (0,2) (0,3) (1,0) (9,0) (19,4) (11,7) (7,17) (6,13) (0,7) (7,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph948",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,10) (6,5) (1,0) (3,9) (1,7) (0,4) (3,6) (8,5) (10,2) (8,0) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph682",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,6) (8,0) (14,17) (8,7) (15,18) (10,9) (3,10) (19,2) (16,15) (11,3) (2,21) (5,17) (1,4) (4,6) (12,8) (17,10) (2,12) (21,20) (20,13) (19,16) (0,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1644",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,0) (2,21) (15,10) (3,4) (6,22) (16,10) (21,8) (13,20) (10,4) (14,18) (13,14) (7,4) (9,8) (20,11) (3,12) (21,1) (15,18) (5,19) (13,6) (13,0) (18,17) (2,3) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1317",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,16) (0,1) (11,4) (8,1) (12,1) (12,14) (13,0) (10,12) (3,0) (0,5) (0,4) (0,6) (4,2) (2,0) (7,0) (3,9) (8,6) (16,2) (15,7) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph317",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,11) (15,12) (14,5) (2,3) (6,1) (7,13) (4,14) (13,8) (9,1) (0,2) (8,6) (10,8) (1,15) (5,9) (3,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1640",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (16,18) (0,17) (2,8) (16,5) (3,12) (7,5) (17,4) (19,21) (10,11) (22,18) (12,17) (7,20) (2,0) (12,14) (13,17) (8,13) (19,1) (7,12) (22,6) (11,9) (0,1) (11,0) (15,11) (12,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1672",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,1) (15,14) (1,17) (14,19) (14,4) (15,7) (10,2) (3,0) (11,3) (9,7) (6,9) (0,2) (6,8) (16,9) (5,12) (9,18) (11,1) (10,17) (13,12) (21,9) (2,20) (7,13) (7,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1763",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,12) (15,22) (4,20) (2,11) (0,1) (14,5) (22,21) (10,13) (2,10) (8,16) (23,6) (0,19) (21,10) (2,0) (18,5) (19,14) (24,7) (8,4) (9,22) (2,1) (13,4) (17,11) (24,3) (9,6) (7,0) (18,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph779",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,21) (15,22) (9,0) (5,14) (1,10) (0,19) (3,16) (7,2) (5,19) (12,14) (17,5) (7,4) (8,7) (22,13) (3,20) (4,6) (13,20) (8,1) (19,10) (17,21) (18,11) (2,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1085",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,2) (6,7) (11,10) (4,3) (0,4) (13,10) (0,2) (1,0) (13,2) (5,0) (3,0) (10,12) (5,1) (5,9) (2,7) (4,11) (7,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph107",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (4,9) (3,10) (7,4) (2,0) (8,7) (8,11) (3,7) (6,10) (11,2) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1769",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,13) (14,19) (0,2) (15,13) (13,12) (19,7) (6,1) (18,21) (17,23) (3,1) (18,14) (9,10) (17,14) (10,16) (2,24) (12,2) (14,4) (17,10) (11,17) (11,8) (16,22) (3,5) (5,2) (0,21) (13,20) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1388",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,4) (1,0) (5,3) (17,8) (0,2) (1,18) (5,14) (0,3) (0,5) (13,5) (0,15) (16,12) (9,10) (7,2) (5,8) (11,5) (18,15) (0,4) (14,7) (6,2) (16,0) (11,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1755",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (9,3) (19,24) (22,15) (0,7) (14,13) (6,22) (1,0) (20,1) (17,12) (23,10) (9,21) (7,23) (12,15) (20,21) (16,4) (8,11) (3,5) (23,8) (12,18) (2,6) (1,13) (4,20) (6,21) (23,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph782",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (9,19) (19,17) (23,22) (7,23) (5,20) (4,15) (19,13) (18,16) (20,7) (0,23) (17,10) (12,4) (22,13) (6,2) (21,15) (13,6) (23,1) (21,13) (14,1) (5,16) (3,21) (11,1) (6,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1391",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,7) (3,0) (12,0) (5,13) (11,8) (4,0) (8,17) (2,14) (16,1) (0,1) (18,9) (4,6) (18,10) (10,3) (13,17) (3,15) (0,11) (11,6) (14,15) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph717",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,13) (19,21) (0,12) (1,16) (3,10) (3,8) (8,11) (3,4) (7,0) (4,16) (14,0) (11,19) (7,15) (18,16) (10,9) (2,17) (11,5) (12,11) (13,2) (18,20) (6,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph269",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,1) (8,1) (4,2) (7,4) (12,8) (14,6) (7,10) (1,0) (3,9) (13,4) (3,12) (12,13) (5,6) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1274",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,16) (13,15) (2,0) (8,6) (11,4) (6,9) (0,6) (12,2) (1,0) (0,7) (8,10) (12,3) (6,14) (1,15) (4,2) (14,13) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1137",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,4) (12,1) (13,7) (0,12) (1,0) (8,11) (6,8) (12,2) (3,12) (3,0) (2,0) (8,13) (5,0) (9,5) (11,5) (10,0) (1,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph348",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,12) (10,0) (11,8) (2,15) (9,0) (5,11) (13,6) (3,8) (5,0) (1,6) (7,6) (2,9) (7,12) (8,14) (12,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph702",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,11) (21,7) (2,20) (1,9) (13,5) (0,1) (10,3) (11,0) (13,0) (17,16) (18,12) (4,6) (14,15) (0,2) (10,7) (17,1) (20,3) (6,11) (8,18) (21,15) (14,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1378",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,5) (0,1) (2,0) (17,16) (9,4) (4,0) (7,14) (11,6) (5,6) (17,2) (9,14) (12,16) (4,2) (16,10) (14,8) (15,13) (1,17) (3,5) (0,14) (3,14) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1779",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,3) (14,8) (19,11) (14,13) (10,5) (12,5) (15,11) (9,21) (1,0) (21,4) (22,6) (23,2) (24,12) (15,6) (24,2) (19,21) (12,6) (17,14) (1,18) (8,7) (7,6) (23,16) (20,14) (14,18) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1102",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,8) (10,8) (13,7) (1,0) (8,5) (4,7) (1,8) (2,12) (7,6) (2,0) (9,5) (2,13) (13,3) (0,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph946",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,7) (2,7) (7,5) (8,2) (9,10) (1,0) (0,4) (6,9) (1,8) (9,4) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph482",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,18) (17,13) (2,6) (11,4) (1,16) (4,7) (6,3) (7,0) (1,14) (6,0) (16,7) (6,13) (13,5) (15,12) (10,1) (17,9) (8,13) (5,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1114",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,7) (6,1) (11,10) (6,2) (12,8) (5,3) (0,11) (9,8) (13,5) (0,1) (13,0) (4,3) (5,12) (10,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1318",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,10) (10,7) (12,16) (15,14) (15,1) (3,0) (16,8) (9,2) (0,2) (5,0) (9,6) (1,3) (1,0) (12,14) (11,13) (4,11) (16,0) (14,6) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph892",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (24,21) (3,22) (22,8) (4,14) (15,13) (16,21) (20,6) (16,10) (14,8) (20,17) (6,8) (11,10) (5,15) (19,5) (23,24) (9,14) (12,7) (10,3) (9,15) (1,3) (2,21) (0,5) (18,15) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1662",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,9) (11,8) (3,0) (15,7) (20,1) (0,10) (9,20) (0,1) (19,2) (15,17) (4,8) (22,8) (2,16) (13,9) (12,2) (9,18) (10,14) (19,1) (15,0) (0,2) (6,13) (5,8) (21,3) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph944",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,6) (9,5) (4,7) (1,8) (3,7) (0,4) (0,1) (1,10) (8,6) (0,3) (6,2) (2,0) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1737",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (23,7) (19,9) (2,0) (21,19) (14,13) (11,14) (15,1) (12,23) (16,3) (12,9) (0,3) (1,0) (1,20) (21,6) (18,16) (4,19) (14,20) (17,11) (3,21) (14,23) (22,13) (16,10) (0,21) (2,5) (20,8) (2,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph118",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,2) (11,3) (1,6) (6,5) (0,4) (7,5) (10,8) (5,9) (8,6) (6,4) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1351",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,5) (6,8) (11,6) (2,0) (4,2) (0,3) (9,4) (12,2) (14,15) (6,5) (16,0) (12,1) (5,10) (9,0) (14,13) (7,5) (1,0) (14,3) (5,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1413",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,12) (4,6) (4,11) (14,7) (9,10) (8,14) (11,15) (18,5) (0,2) (12,16) (3,2) (8,6) (13,9) (14,0) (17,7) (16,0) (1,0) (1,9) (0,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1651",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,9) (19,0) (3,4) (16,7) (6,7) (18,20) (19,16) (13,1) (10,0) (1,0) (14,4) (12,7) (0,2) (22,0) (5,20) (2,17) (17,15) (2,21) (21,3) (11,8) (2,6) (7,8) (13,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph854",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,23) (0,20) (11,15) (13,17) (11,9) (19,2) (21,17) (7,12) (14,19) (4,12) (11,5) (7,10) (20,4) (22,21) (4,19) (2,1) (8,22) (22,16) (0,24) (22,23) (6,5) (9,23) (18,19) (22,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1394",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,12) (15,18) (4,3) (0,1) (18,3) (9,10) (10,3) (18,6) (16,1) (16,17) (2,11) (12,0) (0,3) (4,16) (14,7) (8,0) (2,13) (9,13) (2,0) (7,0) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1037",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,12) (5,4) (5,1) (3,9) (8,1) (10,7) (3,11) (1,0) (0,7) (4,2) (10,6) (5,11) (7,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph185",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,12) (10,13) (11,9) (3,8) (7,5) (0,1) (0,9) (8,5) (3,0) (5,2) (7,4) (10,6) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph631",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,14) (16,8) (13,18) (17,9) (7,3) (4,10) (2,10) (11,12) (5,10) (17,0) (7,0) (5,6) (18,12) (8,12) (20,5) (18,7) (4,19) (9,15) (1,12) (0,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1366",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,0) (8,12) (6,13) (4,7) (2,0) (4,2) (2,1) (16,7) (14,17) (6,12) (9,4) (0,1) (0,14) (16,15) (15,14) (7,3) (6,10) (5,11) (1,11) (0,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph812",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (21,14) (10,14) (16,20) (15,9) (3,7) (3,6) (8,14) (19,0) (4,18) (8,23) (22,23) (13,12) (3,15) (0,22) (4,1) (2,8) (11,15) (20,12) (6,18) (5,2) (12,17) (13,19) (0,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1367",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,10) (13,15) (17,4) (7,16) (16,4) (5,8) (17,9) (0,3) (4,0) (5,1) (5,11) (12,5) (15,3) (13,1) (2,0) (0,1) (5,0) (8,14) (6,3) (15,2) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph263",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,8) (9,14) (5,14) (10,2) (3,13) (10,3) (2,11) (1,4) (0,4) (4,10) (12,10) (7,12) (6,10) (2,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1638",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,3) (11,5) (2,1) (20,0) (6,22) (4,0) (20,4) (19,13) (7,10) (0,2) (3,0) (10,21) (12,7) (19,16) (1,0) (22,18) (19,2) (15,21) (14,11) (22,9) (22,19) (22,0) (17,4) (9,11) (4,12) (8,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1273",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,14) (15,12) (16,7) (2,0) (7,9) (11,4) (0,14) (1,0) (8,2) (16,6) (0,8) (3,12) (1,5) (5,3) (15,11) (1,10) (7,3) (13,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1714",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (7,0) (19,3) (16,11) (22,12) (6,9) (18,2) (1,0) (11,2) (23,7) (18,5) (10,2) (13,4) (20,6) (21,10) (8,4) (13,10) (22,21) (4,17) (14,19) (9,22) (1,2) (0,2) (0,19) (15,8) (5,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph439",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,5) (10,11) (9,16) (15,7) (12,14) (11,15) (1,8) (6,16) (3,14) (1,0) (17,1) (6,2) (14,5) (4,8) (5,1) (4,11) (13,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph500",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,2) (13,12) (5,12) (11,17) (10,0) (8,3) (14,3) (13,14) (17,13) (18,5) (11,7) (1,9) (4,6) (9,15) (15,18) (0,16) (11,16) (14,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1633",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,15) (19,18) (8,20) (0,17) (3,21) (16,14) (8,2) (10,4) (19,22) (4,12) (6,21) (11,15) (16,5) (1,0) (11,9) (20,7) (21,0) (19,21) (1,15) (0,12) (11,13) (22,14) (17,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph302",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,14) (10,11) (7,12) (6,8) (0,12) (10,13) (7,1) (5,2) (11,12) (0,3) (7,4) (7,5) (3,15) (12,8) (9,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph592",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (18,1) (8,13) (18,3) (9,17) (18,2) (16,6) (15,5) (11,17) (3,8) (1,10) (17,10) (16,14) (12,18) (18,7) (4,13) (2,5) (0,19) (16,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph787",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,16) (18,8) (9,23) (1,16) (21,0) (3,10) (7,16) (6,12) (4,17) (11,16) (8,20) (9,15) (9,10) (12,11) (13,10) (19,4) (6,14) (19,3) (5,3) (8,3) (22,8) (13,21) (1,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph998",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,7) (7,4) (7,3) (1,0) (9,0) (6,5) (10,7) (2,0) (9,1) (4,11) (3,0) (8,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph311",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,15) (0,6) (8,9) (14,10) (15,1) (15,5) (2,11) (3,2) (11,8) (4,2) (12,9) (11,7) (8,14) (9,6) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1360",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,7) (3,8) (4,11) (7,16) (2,0) (15,10) (15,17) (9,14) (12,3) (16,17) (12,0) (5,7) (2,13) (2,4) (12,17) (1,9) (1,0) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1281",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,16) (15,4) (2,9) (7,1) (5,7) (15,11) (15,2) (8,10) (16,6) (9,14) (0,5) (16,5) (12,14) (3,8) (13,16) (0,3) (9,13) (2,0) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph968",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,0) (7,9) (0,2) (11,2) (0,3) (5,10) (9,4) (4,10) (6,10) (3,1) (9,8) (1,7) (0,1) (5,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1017",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,7) (10,1) (3,8) (1,0) (4,7) (5,6) (2,0) (3,7) (3,5) (10,9) (1,2) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1057",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (11,8) (0,5) (0,3) (12,8) (12,2) (6,8) (12,3) (5,11) (0,2) (7,5) (4,0) (1,10) (0,1) (9,0) (1,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph681",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (10,1) (4,16) (19,21) (4,8) (18,1) (13,7) (15,4) (7,17) (4,1) (7,4) (17,3) (6,12) (9,21) (21,14) (3,12) (15,0) (17,14) (11,4) (20,1) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph186",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,11) (2,9) (2,7) (10,2) (11,3) (12,10) (4,6) (6,9) (13,5) (2,3) (8,3) (10,1) (1,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph124",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,5) (9,7) (6,1) (4,5) (6,11) (10,7) (12,6) (5,9) (8,3) (2,1) (4,8) (8,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1524",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,0) (0,1) (13,8) (11,18) (14,3) (2,0) (11,19) (16,1) (4,18) (7,1) (6,14) (13,20) (15,8) (16,8) (0,3) (13,5) (17,15) (8,2) (10,3) (11,12) (19,15) (2,10) (15,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph830",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,21) (12,0) (3,6) (6,15) (8,23) (15,19) (20,22) (5,10) (1,12) (5,7) (13,6) (22,23) (11,7) (19,2) (12,16) (2,4) (7,4) (13,23) (12,18) (9,19) (17,2) (14,8) (21,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph227",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,1) (10,12) (13,9) (10,4) (3,2) (2,8) (11,7) (10,5) (13,7) (2,6) (11,12) (7,6) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1086",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,9) (5,4) (0,5) (11,5) (1,0) (8,4) (8,3) (6,8) (6,1) (7,10) (9,7) (9,6) (6,12) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph916",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,0) (8,0) (7,1) (3,9) (5,6) (3,6) (1,0) (4,0) (10,8) (3,0) (5,8) (1,8) (2,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph223",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,9) (11,3) (10,7) (2,4) (12,7) (8,11) (1,11) (8,5) (10,2) (3,2) (2,9) (0,1) (12,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1591",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (18,11) (3,2) (9,19) (5,17) (15,9) (10,11) (15,21) (0,2) (19,10) (13,4) (6,13) (13,11) (14,12) (0,20) (7,3) (10,8) (18,5) (1,14) (1,0) (20,8) (16,21) (19,1) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph657",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,6) (16,17) (18,8) (14,19) (5,14) (3,2) (3,14) (11,6) (16,8) (5,9) (12,9) (14,15) (10,4) (16,20) (10,5) (3,11) (3,7) (10,8) (16,1) (19,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph199",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,6) (4,11) (5,6) (12,4) (6,0) (7,2) (9,0) (8,4) (3,4) (10,3) (1,5) (13,12) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph528",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,0) (14,13) (17,4) (6,18) (3,11) (16,6) (17,6) (12,9) (0,14) (0,18) (13,3) (12,16) (7,0) (2,16) (3,15) (10,9) (10,5) (8,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1079",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,7) (7,10) (8,4) (0,1) (5,6) (4,7) (3,12) (11,12) (6,1) (10,6) (2,11) (0,2) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1682",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,0) (0,1) (17,21) (6,3) (8,23) (6,15) (19,15) (13,23) (14,8) (4,7) (4,2) (12,16) (16,21) (17,2) (23,22) (10,5) (11,7) (22,20) (1,12) (12,18) (6,13) (19,2) (9,19) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1241",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,12) (15,9) (4,8) (0,1) (13,11) (10,0) (0,5) (10,15) (0,3) (15,1) (1,3) (11,4) (8,14) (7,6) (2,9) (12,14) (2,0) (14,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1092",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (7,4) (6,4) (0,9) (3,12) (12,6) (4,9) (3,0) (1,11) (10,13) (8,5) (5,2) (13,2) (8,6) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1743",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (6,9) (20,12) (13,17) (23,4) (0,2) (6,1) (0,3) (19,15) (5,14) (16,12) (21,18) (7,2) (9,2) (23,13) (24,17) (2,11) (0,4) (3,4) (23,11) (23,10) (5,9) (8,23) (12,21) (22,16) (17,15) (12,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph764",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,12) (14,12) (2,1) (14,0) (4,9) (20,17) (7,4) (1,13) (18,22) (6,10) (20,15) (2,4) (15,12) (6,16) (18,15) (7,16) (7,3) (0,19) (14,21) (5,11) (8,12) (22,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1047",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (12,5) (2,5) (11,10) (1,5) (10,7) (1,0) (4,5) (11,0) (3,1) (0,9) (6,8) (6,3) (0,2) (0,3) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph201",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,6) (11,3) (12,5) (5,7) (9,8) (2,8) (6,0) (4,13) (6,4) (9,0) (3,0) (1,5) (10,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph372",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,13) (7,8) (7,0) (9,15) (14,10) (7,14) (1,11) (15,3) (16,9) (13,12) (2,15) (4,9) (6,7) (5,13) (9,0) (0,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1176",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,8) (1,11) (0,2) (5,8) (2,10) (9,11) (12,6) (2,11) (7,12) (2,3) (0,3) (3,13) (0,1) (7,10) (6,14) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph535",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,18) (17,14) (10,15) (4,10) (8,10) (4,1) (18,9) (3,7) (2,3) (15,18) (0,5) (8,6) (3,4) (12,13) (13,0) (13,14) (11,5) (16,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph886",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,20) (15,1) (18,6) (3,20) (5,3) (17,24) (15,8) (11,21) (22,19) (12,9) (16,20) (12,0) (23,6) (8,22) (19,7) (23,24) (17,10) (13,2) (4,2) (24,21) (22,20) (6,14) (0,6) (14,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1405",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (16,15) (10,2) (14,17) (18,8) (2,0) (0,16) (10,5) (6,11) (7,9) (4,0) (5,14) (14,3) (3,11) (10,8) (4,3) (13,14) (5,9) (6,12) (0,3) (3,1) (8,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph724",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,18) (6,7) (0,6) (18,10) (3,4) (3,10) (12,15) (7,11) (11,9) (22,14) (1,22) (5,6) (21,13) (7,21) (20,18) (7,17) (12,17) (2,19) (14,8) (21,19) (19,18) (17,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph759",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,11) (14,16) (3,5) (4,21) (22,2) (6,15) (13,14) (6,7) (2,12) (12,6) (17,14) (19,20) (18,1) (5,12) (6,21) (7,8) (5,10) (14,18) (0,2) (14,8) (19,11) (21,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1074",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,4) (4,0) (1,8) (3,12) (11,8) (12,1) (5,6) (10,4) (0,2) (2,4) (7,9) (3,0) (7,4) (6,3) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1179",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,14) (5,14) (8,4) (0,1) (8,11) (0,6) (13,5) (4,1) (3,9) (3,7) (6,13) (10,7) (7,12) (2,4) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1339",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,17) (11,1) (0,9) (9,16) (15,7) (14,11) (13,14) (0,1) (8,7) (0,12) (15,3) (10,9) (9,4) (2,15) (5,13) (8,13) (0,7) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph115",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,2) (5,8) (1,5) (3,2) (0,8) (2,4) (9,11) (7,11) (4,6) (4,9) (10,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph78",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,7) (4,2) (1,4) (7,8) (6,0) (8,11) (3,5) (8,4) (6,7) (8,9) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph267",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (6,3) (9,11) (12,4) (4,2) (11,6) (10,12) (3,1) (0,7) (13,3) (10,0) (4,14) (3,8) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1319",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,15) (8,7) (13,6) (0,3) (14,11) (2,15) (2,0) (15,4) (11,10) (6,15) (10,0) (4,0) (1,9) (0,1) (2,5) (16,3) (0,8) (13,3) (12,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph489",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (10,9) (4,6) (4,11) (16,12) (11,15) (9,1) (8,6) (3,2) (14,7) (18,5) (0,2) (16,0) (18,0) (14,8) (13,12) (0,14) (13,9) (7,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph477",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,7) (4,0) (14,8) (12,5) (3,2) (14,2) (14,4) (17,15) (1,6) (5,9) (1,8) (12,16) (6,17) (13,11) (13,3) (16,3) (10,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph324",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,7) (1,9) (1,4) (4,12) (3,11) (12,6) (4,7) (4,8) (10,4) (1,14) (3,5) (15,0) (1,13) (2,0) (15,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph504",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,18) (14,11) (9,17) (0,12) (12,10) (4,3) (15,13) (9,12) (6,15) (8,1) (18,3) (5,1) (9,4) (16,6) (16,7) (16,4) (15,8) (13,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph933",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,9) (7,0) (2,10) (5,0) (8,0) (5,3) (1,0) (2,0) (5,10) (3,4) (2,6) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1473",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,14) (0,15) (6,12) (3,5) (13,4) (4,8) (16,1) (0,1) (3,17) (1,9) (0,3) (19,14) (0,2) (10,4) (15,4) (0,4) (11,3) (7,17) (1,4) (18,1) (12,7) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph323",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,10) (9,4) (9,7) (11,3) (8,4) (5,12) (8,3) (12,8) (8,10) (1,0) (13,14) (3,15) (6,2) (1,3) (11,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph953",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,1) (0,2) (10,8) (0,1) (7,6) (7,4) (5,1) (2,6) (0,3) (0,9) (1,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph50",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,9) (2,1) (2,7) (6,0) (5,3) (3,2) (10,1) (3,8) (3,9) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph104",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,11) (6,5) (7,11) (4,2) (0,1) (3,9) (6,2) (1,2) (4,8) (9,5) (1,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph768",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,14) (10,5) (7,3) (1,12) (18,0) (4,10) (22,5) (15,22) (12,11) (2,10) (5,6) (14,0) (18,13) (7,19) (8,17) (21,7) (18,12) (0,20) (12,8) (9,16) (17,9) (21,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph522",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,6) (14,0) (16,12) (14,8) (8,6) (5,18) (4,11) (9,1) (0,2) (13,12) (18,0) (16,0) (14,7) (2,3) (13,9) (9,10) (11,15) (17,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph751",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (2,3) (7,20) (21,22) (2,22) (9,13) (18,0) (14,8) (12,13) (19,14) (5,2) (9,17) (9,1) (11,4) (19,7) (6,4) (11,16) (0,14) (16,12) (0,10) (18,15) (6,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph314",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,12) (3,2) (12,7) (0,15) (13,14) (7,14) (14,8) (1,6) (5,6) (4,10) (3,0) (6,7) (7,10) (11,9) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1048",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,4) (1,5) (11,10) (5,9) (8,2) (0,3) (0,1) (0,2) (7,12) (12,6) (9,12) (10,1) (10,3) (0,11) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph81",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,11) (6,4) (0,5) (1,3) (3,6) (9,0) (8,3) (2,4) (11,6) (9,10) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1721",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,14) (20,23) (17,4) (20,2) (4,0) (12,5) (3,15) (13,15) (8,5) (18,21) (9,17) (9,6) (0,2) (10,16) (1,0) (15,7) (16,21) (9,11) (3,18) (3,0) (4,3) (13,1) (0,5) (6,22) (15,2) (8,19) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph173",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,4) (0,7) (9,10) (2,4) (6,7) (8,2) (0,11) (1,3) (9,12) (1,10) (5,3) (10,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1568",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (21,10) (14,17) (21,16) (13,14) (0,10) (13,10) (0,2) (2,6) (11,0) (8,5) (16,12) (12,1) (19,5) (14,5) (20,7) (19,4) (20,9) (18,4) (0,15) (10,6) (7,3) (3,4) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph544",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,4) (7,0) (7,5) (12,8) (16,10) (17,14) (1,16) (17,2) (16,17) (15,14) (18,10) (6,17) (18,11) (12,9) (5,3) (7,8) (13,17) (11,12) (19,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph122",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,0) (9,0) (12,11) (2,7) (4,3) (7,3) (10,4) (1,5) (3,6) (4,8) (6,5) (12,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph931",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,4) (4,6) (1,0) (2,9) (7,10) (3,5) (0,2) (10,2) (0,6) (0,3) (0,4) (1,3) (0,10) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1648",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,15) (14,6) (0,6) (13,2) (22,0) (3,20) (20,21) (0,2) (7,19) (10,17) (21,11) (3,0) (13,14) (6,18) (5,3) (8,16) (0,12) (22,19) (12,9) (4,20) (1,0) (6,15) (4,2) (17,20) (8,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph991",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (2,0) (4,11) (8,1) (3,10) (1,9) (4,8) (8,5) (2,10) (0,1) (8,0) (0,7) (6,3) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1517",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,11) (0,3) (17,5) (9,11) (10,20) (12,7) (18,13) (16,1) (12,19) (6,9) (8,13) (13,2) (4,12) (16,10) (15,8) (17,3) (0,7) (4,20) (0,1) (0,2) (16,8) (5,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph667",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,18) (12,16) (0,3) (4,11) (1,18) (15,21) (13,21) (3,20) (8,0) (17,12) (17,6) (13,1) (0,19) (2,5) (10,11) (16,14) (19,12) (14,7) (10,8) (8,15) (13,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1705",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,13) (3,6) (22,23) (18,12) (10,5) (16,21) (7,11) (12,16) (0,12) (1,12) (21,17) (0,1) (2,4) (8,14) (5,7) (19,2) (2,0) (3,0) (9,19) (22,20) (17,2) (23,8) (6,15) (4,0) (15,19) (23,13) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph846",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,9) (24,21) (14,6) (4,9) (18,23) (18,10) (20,12) (24,9) (15,0) (15,12) (22,11) (16,19) (0,13) (5,23) (1,7) (19,0) (21,10) (22,5) (15,17) (0,7) (2,20) (8,4) (21,14) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph794",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,12) (18,0) (11,10) (14,12) (13,17) (11,9) (0,23) (18,16) (19,22) (7,5) (16,5) (12,7) (11,0) (15,11) (8,13) (19,1) (12,1) (3,12) (20,17) (7,21) (4,17) (6,22) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph980",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,2) (2,4) (1,7) (5,0) (7,4) (8,11) (1,0) (6,5) (10,0) (9,2) (9,3) (5,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1492",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,12) (8,11) (15,5) (14,11) (3,10) (0,4) (0,16) (2,0) (0,6) (0,1) (14,10) (7,3) (8,19) (1,13) (4,11) (7,5) (6,2) (3,0) (16,9) (7,17) (1,4) (12,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1739",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (10,21) (0,3) (21,2) (1,8) (22,9) (17,2) (5,4) (20,12) (7,18) (6,23) (7,20) (13,4) (23,4) (8,21) (1,0) (4,16) (19,23) (5,11) (6,17) (13,0) (15,21) (0,2) (14,7) (5,20) (9,0) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph432",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (5,12) (0,7) (10,2) (14,0) (14,4) (7,15) (4,10) (3,7) (1,12) (4,16) (17,10) (8,13) (6,5) (12,8) (11,9) (9,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph276",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,5) (11,14) (9,2) (2,3) (1,10) (12,3) (8,3) (11,0) (13,10) (4,6) (6,9) (2,10) (11,1) (2,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1506",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,13) (8,11) (14,11) (17,10) (17,7) (17,0) (12,1) (1,19) (20,16) (18,19) (1,0) (0,11) (9,11) (0,4) (12,3) (15,12) (0,2) (7,12) (17,4) (3,0) (6,13) (5,16) (2,8) (7,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1139",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,9) (4,1) (0,1) (13,8) (11,1) (13,3) (4,12) (3,0) (13,7) (3,6) (2,0) (10,8) (0,4) (11,2) (5,12) (5,10) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1166",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,13) (9,2) (0,2) (5,14) (1,5) (8,9) (7,2) (7,11) (6,5) (4,7) (1,2) (11,3) (3,10) (0,1) (3,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph934",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,3) (8,6) (3,0) (1,4) (1,7) (0,1) (0,2) (10,5) (9,0) (2,4) (8,5) (3,2) (1,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph158",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,4) (10,11) (2,12) (5,4) (8,12) (11,8) (12,3) (1,6) (8,0) (6,4) (9,11) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1658",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,3) (4,5) (18,22) (17,11) (4,2) (12,9) (20,15) (13,19) (22,17) (1,0) (6,7) (9,16) (3,21) (13,5) (16,6) (7,20) (10,1) (10,22) (8,17) (16,17) (17,0) (6,14) (4,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1788",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,1) (2,0) (1,7) (17,15) (6,9) (18,2) (4,5) (14,10) (5,23) (5,19) (9,3) (8,7) (21,2) (1,0) (12,1) (20,0) (20,7) (15,14) (22,12) (23,13) (18,9) (4,24) (16,8) (11,4) (0,13) (0,3) (4,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph19",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (0,9) (4,8) (5,2) (7,0) (3,8) (7,6) (8,2) (8,1) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1510",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,0) (0,2) (3,2) (6,1) (7,11) (18,8) (20,4) (10,20) (5,0) (19,1) (0,17) (17,15) (18,9) (16,12) (7,20) (3,0) (1,16) (4,13) (0,4) (2,18) (1,0) (10,2) (5,12) (18,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph438",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,9) (9,7) (16,0) (16,3) (6,14) (2,14) (12,4) (14,17) (10,7) (4,1) (1,6) (1,5) (11,13) (8,11) (8,14) (16,4) (0,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph571",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,0) (2,15) (12,11) (1,8) (3,9) (2,6) (13,8) (17,14) (15,7) (18,2) (19,18) (10,16) (4,6) (8,10) (5,7) (9,2) (11,8) (7,17) (12,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1296",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,1) (10,3) (15,2) (1,0) (16,11) (0,2) (5,13) (4,11) (9,12) (10,11) (7,10) (8,2) (5,0) (3,6) (6,12) (0,3) (13,10) (8,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1010",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,8) (0,1) (3,0) (2,11) (5,7) (5,6) (1,4) (8,9) (4,11) (5,0) (0,6) (2,0) (10,2) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1242",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,0) (9,0) (7,8) (5,13) (0,4) (3,15) (14,7) (0,2) (15,2) (15,9) (0,7) (1,0) (7,6) (1,11) (11,0) (9,4) (8,13) (13,12) (10,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1496",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,11) (0,19) (14,19) (1,10) (11,12) (0,3) (8,16) (0,2) (4,0) (9,13) (17,13) (6,14) (6,1) (5,0) (18,2) (8,14) (9,18) (4,6) (5,6) (0,1) (7,6) (12,15) (18,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1346",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,9) (1,0) (6,1) (7,5) (11,15) (13,12) (10,9) (2,0) (2,11) (6,8) (4,2) (17,11) (14,17) (13,5) (14,16) (5,1) (16,12) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph918",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,3) (5,1) (0,3) (7,5) (2,0) (4,2) (8,10) (1,0) (0,7) (4,5) (8,1) (10,6) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1329",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,0) (10,0) (1,12) (15,4) (6,2) (5,4) (13,17) (7,3) (13,14) (3,4) (9,0) (10,14) (10,6) (5,14) (16,7) (11,16) (8,5) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph214",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,13) (9,13) (2,3) (0,1) (10,4) (5,10) (12,10) (6,2) (2,8) (6,7) (11,12) (1,9) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph936",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,0) (4,1) (2,0) (10,9) (0,3) (5,10) (9,1) (2,10) (8,7) (10,0) (0,1) (9,3) (10,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1455",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (10,18) (12,14) (0,6) (1,7) (5,9) (15,12) (14,2) (9,16) (5,19) (8,0) (7,4) (17,15) (3,2) (0,1) (0,13) (10,5) (0,4) (19,11) (4,9) (0,15) (3,0) (17,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph73",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (9,5) (0,3) (11,2) (7,3) (3,10) (5,7) (1,5) (8,3) (11,9) (4,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph754",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,6) (8,21) (4,6) (3,0) (7,20) (11,9) (9,13) (19,13) (11,12) (6,5) (17,14) (9,18) (8,14) (16,1) (1,6) (20,12) (15,0) (18,2) (22,6) (14,19) (18,3) (10,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1571",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,13) (6,20) (2,0) (6,16) (3,17) (19,8) (2,4) (5,9) (4,5) (4,7) (1,3) (5,12) (0,3) (18,12) (14,13) (19,4) (15,14) (0,6) (0,1) (6,19) (7,10) (4,17) (20,11) (0,4) (21,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1744",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,14) (3,2) (21,1) (16,13) (11,13) (14,23) (5,15) (12,23) (19,11) (7,14) (6,10) (0,4) (8,1) (3,17) (18,12) (20,21) (0,1) (2,0) (3,16) (9,24) (14,8) (10,24) (5,22) (6,20) (22,17) (2,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1390",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,8) (0,2) (5,9) (15,6) (0,4) (3,14) (0,3) (17,2) (11,4) (0,1) (5,6) (6,16) (1,13) (0,15) (9,18) (1,2) (14,1) (13,4) (10,12) (1,12) (7,2) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph939",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,1) (0,3) (5,1) (6,5) (9,7) (2,8) (0,1) (3,9) (6,0) (0,8) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph480",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,18) (16,3) (0,14) (8,10) (2,16) (8,13) (11,5) (1,17) (5,17) (14,10) (11,15) (1,3) (7,13) (12,15) (3,4) (6,18) (7,9) (17,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph845",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,6) (4,0) (5,17) (9,23) (12,3) (13,14) (17,23) (3,16) (2,22) (18,24) (0,8) (9,20) (0,18) (21,12) (19,20) (24,23) (7,23) (15,16) (14,0) (11,2) (10,24) (22,16) (24,1) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph990",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,10) (0,1) (0,8) (4,6) (2,4) (2,0) (5,2) (3,2) (9,4) (8,5) (5,1) (11,9) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1265",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,3) (3,0) (4,16) (5,4) (8,16) (4,15) (2,0) (6,16) (13,10) (4,1) (9,6) (0,1) (13,7) (16,14) (0,10) (5,11) (15,3) (7,6) (2,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph912",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,1) (4,8) (9,1) (8,10) (3,7) (10,0) (2,0) (0,3) (0,1) (4,5) (2,7) (4,6) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1004",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,3) (4,1) (7,4) (4,2) (11,6) (0,1) (1,11) (2,3) (2,10) (2,0) (11,9) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1531",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,0) (10,7) (4,7) (1,8) (9,3) (17,12) (13,19) (15,0) (19,8) (20,17) (0,8) (0,3) (18,16) (6,11) (15,20) (2,0) (10,2) (6,3) (16,0) (17,4) (7,14) (9,15) (0,1) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1371",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,16) (11,9) (15,2) (6,16) (14,6) (1,8) (15,8) (3,0) (3,4) (14,3) (2,9) (14,5) (10,5) (1,0) (0,17) (16,12) (7,16) (12,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1116",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,6) (11,4) (2,9) (8,3) (3,7) (0,11) (13,5) (2,0) (11,12) (1,5) (0,1) (10,3) (0,7) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph954",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,2) (3,0) (8,10) (7,4) (1,6) (1,0) (5,10) (3,9) (0,2) (6,4) (3,7) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1035",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,1) (0,1) (6,11) (11,7) (2,0) (2,6) (3,6) (0,10) (7,5) (12,4) (3,0) (1,8) (1,5) (11,10) (5,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1684",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,8) (22,1) (22,10) (5,19) (2,21) (8,2) (10,3) (16,0) (0,3) (21,14) (10,11) (7,11) (13,5) (10,20) (1,17) (15,12) (6,3) (0,23) (20,13) (10,9) (0,2) (6,12) (18,0) (11,8) (16,4) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph900",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,0) (6,4) (0,1) (1,5) (7,9) (1,8) (0,5) (5,7) (3,6) (1,6) (0,10) (2,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1106",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,7) (1,13) (12,6) (2,13) (2,3) (7,8) (3,9) (4,8) (1,0) (0,2) (7,10) (0,3) (9,12) (13,8) (11,7) (13,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph374",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,0) (5,1) (7,9) (5,3) (6,14) (4,2) (11,16) (9,11) (0,14) (12,5) (0,3) (5,13) (5,10) (8,15) (5,8) (2,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph648",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,17) (13,12) (12,16) (14,0) (9,14) (6,3) (20,11) (10,15) (2,8) (0,15) (1,4) (4,18) (12,18) (3,15) (2,5) (14,20) (19,13) (3,7) (15,8) (0,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph46",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,7) (10,9) (7,1) (7,10) (2,9) (8,7) (3,1) (5,4) (4,1) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1401",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,7) (0,3) (1,15) (4,14) (4,0) (0,5) (17,7) (15,0) (7,4) (4,10) (18,17) (13,4) (5,3) (1,0) (9,1) (2,0) (11,3) (8,4) (12,6) (1,16) (4,1) (3,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1188",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,10) (10,3) (12,14) (13,11) (5,8) (7,2) (0,4) (14,5) (13,12) (1,2) (0,1) (9,1) (9,5) (12,6) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1777",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (13,22) (10,5) (7,6) (2,24) (0,20) (3,0) (22,16) (1,0) (0,17) (3,5) (9,8) (17,4) (12,21) (2,11) (15,1) (10,6) (0,2) (22,2) (15,11) (14,10) (11,19) (5,23) (0,16) (9,10) (20,10) (12,14) (15,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph570",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,18) (18,8) (16,2) (6,0) (11,19) (9,14) (0,4) (15,5) (1,17) (17,9) (11,3) (13,7) (7,3) (2,10) (8,10) (17,6) (12,16) (15,13) (19,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1572",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,0) (6,2) (0,17) (10,20) (11,19) (10,1) (4,21) (15,11) (9,8) (12,0) (5,2) (15,16) (7,15) (6,4) (3,0) (0,19) (3,14) (1,0) (16,1) (3,10) (4,17) (18,16) (1,13) (7,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph861",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (11,10) (23,3) (22,12) (2,4) (8,1) (10,7) (19,10) (11,4) (9,7) (24,6) (14,24) (8,20) (15,13) (2,17) (17,21) (7,20) (22,21) (15,0) (15,10) (11,5) (11,3) (2,16) (17,18) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1395",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,13) (8,12) (18,10) (14,17) (11,17) (6,17) (0,7) (11,12) (5,3) (17,2) (5,7) (15,16) (0,2) (0,1) (1,16) (16,10) (18,12) (8,7) (9,17) (7,4) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1027",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,1) (11,7) (8,4) (0,2) (12,7) (12,3) (1,7) (2,9) (1,0) (5,12) (12,9) (7,10) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph410",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,12) (1,12) (5,16) (7,5) (7,13) (11,6) (9,12) (16,15) (11,0) (8,11) (3,12) (10,11) (4,13) (14,1) (0,12) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph935",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,2) (10,8) (8,0) (5,0) (0,6) (2,0) (2,9) (7,4) (5,3) (1,0) (3,0) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1289",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,3) (2,16) (8,1) (6,9) (1,0) (0,13) (7,15) (5,0) (7,0) (1,12) (2,0) (12,10) (14,12) (9,3) (8,6) (4,2) (4,11) (14,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph739",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,13) (15,2) (12,22) (16,17) (11,3) (12,0) (1,18) (7,11) (4,18) (14,9) (15,6) (1,10) (1,20) (12,6) (1,5) (11,0) (19,22) (20,11) (8,13) (9,21) (2,17) (21,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1537",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,10) (1,8) (17,3) (5,12) (19,6) (14,2) (7,20) (4,14) (1,20) (16,3) (11,12) (18,17) (8,14) (4,0) (2,0) (7,10) (13,16) (11,13) (2,3) (0,1) (15,5) (14,9) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph166",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,8) (6,7) (6,5) (3,8) (2,6) (10,5) (0,12) (5,0) (4,1) (9,5) (4,11) (11,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1719",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,16) (1,15) (1,0) (2,0) (0,6) (14,22) (8,23) (4,0) (7,3) (3,10) (8,11) (11,21) (11,19) (5,7) (23,13) (10,14) (22,12) (16,9) (21,1) (22,4) (0,17) (7,20) (3,0) (18,4) (6,2) (12,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph984",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,0) (1,3) (0,3) (7,3) (2,4) (2,0) (6,11) (10,9) (1,0) (4,6) (8,3) (3,6) (0,5) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1024",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,7) (0,3) (3,2) (8,2) (10,4) (1,0) (1,9) (7,11) (6,2) (11,10) (2,0) (7,6) (5,0) (9,12) (0,4) (10,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1549",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,15) (18,10) (18,7) (2,18) (12,18) (9,17) (6,16) (5,2) (1,19) (17,11) (4,13) (20,0) (5,15) (16,14) (17,20) (18,3) (10,1) (8,3) (0,1) (8,13) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph888",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (16,20) (6,0) (14,13) (3,5) (4,2) (20,4) (8,22) (19,7) (11,21) (6,18) (19,22) (0,12) (17,10) (24,23) (22,20) (2,13) (6,23) (15,1) (3,20) (8,15) (12,9) (24,21) (24,17) (6,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1284",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,7) (15,2) (10,16) (0,2) (15,11) (16,6) (13,16) (2,9) (15,4) (9,13) (8,10) (5,7) (0,5) (12,14) (3,8) (5,16) (9,14) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1428",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,0) (13,5) (0,3) (2,7) (0,1) (5,3) (10,9) (5,14) (18,1) (6,2) (11,9) (5,11) (12,16) (2,0) (16,0) (17,8) (5,8) (0,15) (18,15) (14,7) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph585",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,12) (2,18) (18,13) (14,17) (6,1) (18,8) (18,9) (11,7) (15,1) (2,3) (4,0) (1,0) (10,1) (7,16) (2,10) (4,17) (16,0) (12,5) (19,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph784",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,10) (2,13) (8,11) (9,13) (15,7) (1,16) (12,11) (11,19) (0,4) (0,19) (18,21) (22,3) (18,16) (12,17) (0,7) (4,16) (14,0) (8,3) (10,9) (20,2) (4,23) (6,18) (5,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph750",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,8) (9,3) (15,22) (7,2) (1,9) (13,21) (7,5) (14,9) (19,10) (20,6) (10,20) (12,16) (20,15) (17,14) (13,7) (11,14) (0,13) (17,2) (16,14) (8,6) (16,4) (17,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph838",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,11) (3,14) (11,3) (4,5) (2,1) (8,20) (17,13) (0,10) (6,1) (13,20) (7,2) (4,12) (10,2) (17,2) (17,12) (19,13) (6,16) (23,13) (21,2) (1,9) (16,18) (15,1) (22,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph363",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,7) (16,8) (1,3) (0,5) (5,15) (8,6) (8,14) (11,15) (10,3) (9,14) (14,2) (10,15) (12,5) (6,7) (9,13) (15,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph513",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,10) (8,1) (17,2) (12,4) (16,14) (9,12) (11,7) (7,18) (11,0) (15,14) (9,7) (6,9) (2,10) (6,5) (13,9) (7,15) (13,1) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1271",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,7) (0,1) (0,2) (1,11) (0,11) (10,14) (13,12) (2,15) (9,4) (7,8) (3,15) (16,9) (15,9) (7,0) (9,0) (13,5) (13,8) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph344",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,10) (15,13) (4,9) (12,0) (7,6) (14,0) (8,12) (14,15) (11,1) (2,4) (4,7) (7,3) (11,5) (12,6) (1,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph150",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,3) (8,1) (12,9) (2,9) (8,5) (6,0) (10,12) (4,12) (7,9) (6,12) (8,4) (11,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1458",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,16) (6,19) (6,1) (18,3) (9,6) (12,7) (15,11) (11,8) (7,9) (19,14) (16,4) (8,14) (13,4) (1,4) (18,14) (0,2) (0,16) (1,0) (1,10) (2,14) (17,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1403",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,6) (12,7) (14,8) (18,3) (17,0) (10,1) (6,14) (6,9) (16,4) (13,4) (16,0) (14,18) (14,2) (1,0) (7,9) (11,8) (5,16) (11,15) (1,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph11",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,10) (3,4) (0,9) (10,6) (8,7) (8,9) (10,8) (3,5) (2,1) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph14",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,4) (8,6) (0,1) (9,2) (4,3) (4,1) (4,9) (10,1) (10,5) (3,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph6",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,6) (8,5) (4,0) (8,0) (8,1) (8,10) (1,7) (10,2) (9,3) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1754",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (17,10) (19,16) (10,15) (0,8) (0,1) (21,0) (2,1) (23,12) (20,24) (19,11) (18,12) (9,13) (18,4) (13,20) (12,3) (15,9) (16,7) (22,5) (11,12) (3,20) (5,16) (6,19) (11,1) (14,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph5",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,4) (0,4) (2,8) (1,8) (6,9) (2,7) (5,7) (10,9) (3,1) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph62",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (5,4) (3,0) (5,10) (0,6) (8,2) (1,5) (8,0) (6,1) (9,7) (11,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph981",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (5,7) (0,4) (8,2) (4,6) (10,8) (5,6) (5,9) (8,6) (0,1) (2,0) (11,5) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1187",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,13) (11,2) (11,12) (3,0) (9,4) (3,10) (4,0) (0,1) (12,7) (7,3) (12,13) (1,8) (0,2) (13,6) (5,1) (14,5) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph180",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,1) (8,7) (6,5) (3,13) (3,10) (2,4) (3,11) (12,0) (4,1) (3,5) (9,8) (4,7) (9,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1594",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,21) (16,14) (10,1) (18,6) (5,15) (3,0) (20,1) (16,4) (0,1) (8,21) (2,0) (13,0) (13,3) (15,16) (5,2) (9,17) (18,20) (8,12) (17,7) (21,17) (18,2) (3,18) (18,11) (19,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1054",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,1) (10,11) (2,7) (4,2) (9,0) (3,6) (8,7) (5,10) (12,5) (2,11) (1,11) (0,3) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1130",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,13) (6,8) (4,13) (0,2) (0,3) (0,4) (1,13) (2,3) (3,10) (1,0) (11,8) (8,4) (12,13) (3,13) (5,8) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph634",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (17,12) (0,20) (12,1) (14,2) (13,20) (4,2) (19,11) (20,12) (19,16) (0,10) (19,9) (6,15) (4,18) (9,5) (3,17) (16,7) (6,8) (0,14) (7,0) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1404",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,8) (13,12) (7,0) (12,1) (0,9) (17,16) (15,14) (4,0) (9,10) (2,0) (6,11) (1,0) (16,7) (2,4) (0,14) (3,17) (6,8) (3,0) (18,5) (0,5) (12,4) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph437",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,16) (3,14) (6,8) (15,14) (12,1) (6,5) (0,3) (2,4) (14,13) (9,4) (5,17) (5,10) (0,16) (0,9) (11,6) (7,5) (12,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph891",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,21) (19,2) (6,3) (8,4) (16,13) (6,14) (23,16) (12,22) (5,19) (5,23) (8,23) (23,11) (18,0) (14,17) (15,11) (0,1) (23,14) (20,11) (1,22) (7,16) (5,1) (22,9) (1,24) (15,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph475",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,2) (4,6) (11,8) (7,5) (15,7) (15,17) (11,12) (16,7) (15,0) (8,2) (9,2) (9,3) (1,8) (12,5) (17,13) (8,10) (10,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph52",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,0) (2,3) (7,5) (3,7) (0,7) (9,1) (6,7) (8,5) (9,8) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph484",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,2) (10,11) (10,8) (17,3) (17,6) (1,12) (16,14) (14,7) (15,12) (1,13) (3,0) (0,13) (18,8) (0,8) (9,18) (11,4) (16,12) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph607",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,5) (0,2) (9,1) (17,3) (9,8) (19,16) (5,13) (13,6) (7,14) (11,2) (13,14) (9,12) (15,3) (20,14) (14,18) (5,11) (10,7) (17,8) (16,4) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1539",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,0) (1,0) (8,14) (4,2) (11,7) (15,18) (12,8) (19,20) (19,9) (19,13) (19,2) (6,13) (4,7) (3,0) (5,10) (0,2) (1,12) (16,12) (17,2) (15,6) (0,4) (3,6) (16,17) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1663",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,12) (9,18) (20,2) (16,9) (9,7) (10,17) (6,9) (0,1) (15,7) (22,0) (10,7) (17,1) (12,13) (15,14) (8,6) (1,11) (2,10) (0,2) (3,11) (9,21) (7,13) (4,14) (19,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1446",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (3,8) (13,0) (10,15) (4,3) (16,13) (19,6) (0,5) (11,18) (14,18) (6,13) (12,5) (4,1) (4,10) (9,10) (2,3) (0,1) (2,17) (8,7) (0,2) (15,18) (13,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1310",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,6) (16,7) (0,2) (5,0) (10,9) (15,13) (4,9) (0,3) (8,5) (2,15) (15,3) (1,0) (16,4) (1,5) (1,13) (4,0) (6,3) (12,5) (14,8) (5,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph120",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,3) (9,0) (1,2) (10,12) (10,5) (7,10) (8,2) (4,3) (7,4) (8,11) (2,10) (8,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph337",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,14) (11,12) (5,0) (2,1) (8,9) (7,15) (12,10) (4,7) (0,13) (5,11) (1,11) (9,13) (3,0) (12,15) (10,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph177",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,2) (3,8) (10,5) (0,5) (0,12) (8,6) (7,6) (11,4) (1,4) (9,5) (6,5) (11,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph613",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,20) (15,10) (7,16) (0,18) (12,17) (19,4) (19,16) (12,11) (1,11) (0,6) (18,3) (13,9) (10,14) (12,20) (16,5) (2,1) (0,5) (7,8) (15,9) (19,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph538",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,12) (3,11) (13,14) (1,0) (14,0) (3,13) (15,3) (9,12) (17,6) (4,17) (8,2) (7,0) (6,16) (5,10) (0,18) (9,10) (2,16) (6,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph614",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,0) (10,7) (19,6) (5,12) (13,11) (13,16) (14,2) (14,9) (12,11) (3,16) (10,6) (1,8) (18,17) (20,7) (5,15) (3,2) (14,8) (4,14) (3,17) (20,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph579",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,10) (8,2) (3,17) (2,13) (13,5) (10,12) (15,6) (8,4) (14,15) (19,2) (8,7) (16,9) (1,19) (9,3) (9,1) (0,3) (0,15) (9,11) (18,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1554",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,3) (4,0) (15,18) (20,8) (0,3) (9,3) (19,2) (14,13) (6,13) (1,0) (4,10) (6,20) (0,2) (0,13) (18,14) (16,5) (15,10) (12,18) (0,5) (7,8) (2,3) (17,13) (1,4) (11,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph817",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,2) (8,12) (7,3) (23,22) (6,17) (13,10) (19,22) (19,16) (3,11) (10,20) (0,11) (21,3) (4,23) (0,8) (9,8) (10,22) (16,15) (6,5) (1,4) (17,18) (15,2) (14,20) (22,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1604",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (4,9) (1,0) (7,0) (20,10) (21,14) (12,21) (8,13) (20,12) (17,5) (3,17) (16,10) (11,6) (16,8) (13,18) (5,9) (15,8) (7,12) (2,13) (19,21) (0,3) (1,16) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1566",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,0) (4,12) (8,20) (0,3) (12,0) (4,10) (14,16) (19,20) (16,5) (13,11) (21,19) (1,15) (19,14) (11,9) (0,21) (0,17) (18,7) (1,0) (7,17) (11,15) (8,15) (21,6) (8,2) (4,0) (3,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1688",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,19) (2,0) (23,0) (22,23) (13,21) (1,14) (6,13) (23,7) (19,9) (3,21) (4,15) (8,6) (1,0) (16,18) (20,5) (22,13) (0,3) (10,17) (12,4) (1,11) (4,0) (23,1) (15,21) (20,7) (19,13) (5,16) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1144",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,2) (1,14) (6,3) (0,2) (0,1) (6,5) (4,13) (0,4) (11,8) (3,1) (1,11) (12,2) (7,8) (3,0) (9,8) (10,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1791",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,11) (11,15) (14,4) (7,17) (17,0) (11,16) (19,21) (21,6) (21,3) (21,0) (22,19) (15,1) (1,0) (8,15) (8,2) (7,23) (16,5) (0,12) (12,13) (24,14) (19,4) (10,4) (20,8) (22,20) (14,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph287",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,0) (2,12) (10,9) (3,5) (4,11) (9,14) (13,4) (1,14) (8,7) (6,10) (1,3) (2,13) (0,11) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph222",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,7) (1,12) (8,2) (11,12) (11,10) (1,7) (11,4) (7,2) (5,9) (10,5) (12,6) (3,0) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1282",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,15) (2,11) (13,5) (16,12) (1,5) (11,14) (3,0) (8,6) (9,10) (4,2) (0,1) (14,16) (2,0) (13,12) (8,9) (2,3) (6,1) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1227",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,14) (14,4) (13,11) (9,5) (5,12) (1,6) (2,0) (1,8) (14,7) (12,3) (8,14) (6,15) (11,10) (0,4) (2,3) (3,13) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph56",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,6) (3,4) (1,2) (10,2) (1,0) (2,7) (9,10) (4,7) (8,5) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1253",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,0) (0,1) (3,9) (11,6) (13,0) (0,5) (10,4) (6,14) (8,12) (15,11) (10,3) (0,6) (9,2) (13,3) (14,12) (2,0) (7,2) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1232",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,0) (3,0) (15,2) (1,13) (11,5) (3,14) (4,9) (5,8) (15,4) (9,7) (5,10) (6,9) (2,0) (12,8) (15,13) (6,3) (5,1) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1362",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (11,0) (0,17) (13,9) (0,3) (17,9) (7,13) (15,2) (1,8) (11,3) (5,11) (15,10) (12,1) (15,6) (12,6) (0,1) (14,2) (1,4) (1,11) (0,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph683",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,10) (17,6) (5,14) (1,2) (8,12) (7,21) (18,2) (10,13) (19,0) (9,21) (6,9) (13,4) (11,2) (14,19) (0,7) (5,18) (15,11) (19,3) (10,20) (8,4) (16,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1512",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (10,16) (20,9) (16,11) (5,20) (3,7) (8,4) (5,1) (17,16) (16,15) (2,0) (19,20) (15,6) (14,15) (9,14) (2,20) (18,0) (20,7) (5,12) (19,13) (17,8) (0,1) (10,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1708",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (11,23) (0,2) (10,7) (1,0) (14,16) (22,4) (9,8) (4,0) (6,13) (7,14) (9,12) (18,15) (11,21) (0,3) (22,2) (5,0) (14,19) (4,16) (5,13) (3,17) (2,20) (8,17) (5,22) (23,3) (13,23) (9,1) (15,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph542",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,19) (7,1) (6,16) (2,9) (3,14) (7,4) (14,12) (2,17) (15,8) (18,1) (5,9) (9,19) (2,12) (6,9) (13,2) (15,2) (11,8) (0,14) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph866",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,18) (15,6) (24,19) (2,5) (16,18) (21,4) (23,6) (10,11) (7,24) (0,22) (17,24) (1,0) (0,8) (12,1) (8,15) (15,2) (24,10) (23,20) (17,13) (13,23) (18,3) (21,11) (14,4) (8,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1224",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,5) (3,14) (1,12) (14,12) (9,4) (0,3) (0,4) (13,14) (0,1) (6,11) (5,6) (2,4) (0,2) (6,8) (0,15) (5,2) (0,9) (10,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1720",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,22) (20,10) (0,16) (19,11) (23,22) (9,10) (18,15) (12,14) (2,12) (20,0) (0,1) (5,3) (2,11) (6,7) (1,15) (9,8) (10,14) (22,13) (5,21) (10,6) (17,0) (10,5) (17,4) (11,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph587",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (12,16) (13,19) (14,9) (10,16) (16,8) (13,9) (10,17) (17,7) (2,18) (5,19) (2,9) (1,5) (14,15) (5,11) (6,15) (18,0) (7,3) (15,16) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1325",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,3) (5,13) (3,0) (1,0) (11,2) (11,1) (16,15) (17,1) (6,3) (9,17) (17,7) (16,10) (4,14) (16,7) (13,8) (12,1) (0,2) (4,8) (14,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1793",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,1) (2,0) (19,0) (24,3) (2,11) (21,22) (7,24) (1,0) (6,23) (0,4) (9,22) (0,3) (18,2) (5,18) (13,4) (22,15) (5,14) (11,17) (10,2) (19,14) (7,0) (9,6) (13,10) (10,21) (12,19) (8,16) (20,4) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1268",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,9) (16,15) (4,7) (3,0) (10,2) (8,1) (15,9) (15,0) (0,8) (14,8) (11,6) (2,0) (0,1) (7,12) (10,7) (4,16) (3,6) (13,0) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph321",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,13) (1,8) (15,14) (5,2) (10,2) (10,12) (2,8) (3,4) (11,7) (14,5) (4,13) (2,0) (4,11) (6,9) (10,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1088",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,3) (6,0) (1,2) (9,7) (4,7) (3,12) (13,3) (1,7) (0,11) (6,2) (0,1) (13,8) (10,0) (5,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1767",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (8,23) (13,5) (11,5) (11,15) (3,8) (16,13) (20,0) (1,0) (12,14) (18,1) (10,15) (17,1) (2,7) (1,6) (21,13) (23,1) (19,4) (24,2) (22,20) (0,14) (14,11) (12,17) (9,16) (7,0) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1245",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,8) (7,15) (9,15) (3,15) (3,5) (0,4) (4,1) (13,12) (2,0) (3,0) (0,12) (15,13) (2,8) (1,0) (2,4) (0,14) (10,12) (11,6) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1637",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (9,1) (0,16) (8,21) (14,15) (13,22) (17,19) (19,15) (4,6) (14,4) (1,2) (18,21) (20,0) (0,1) (22,5) (10,3) (19,11) (13,17) (9,22) (19,12) (13,16) (11,7) (11,18) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph137",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (6,5) (8,4) (7,2) (5,1) (4,12) (0,9) (0,6) (11,12) (7,3) (4,3) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1288",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,16) (0,4) (7,0) (9,3) (16,14) (10,12) (5,0) (1,0) (15,7) (4,11) (2,4) (0,3) (13,0) (6,8) (14,12) (0,2) (1,12) (8,1) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph678",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,17) (1,8) (6,20) (21,7) (10,12) (15,10) (4,11) (11,5) (10,7) (15,9) (14,17) (2,4) (7,8) (0,15) (3,11) (10,11) (21,18) (13,2) (16,7) (19,17) (3,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph864",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (11,8) (16,4) (0,7) (19,0) (0,14) (4,23) (9,13) (20,2) (12,17) (7,15) (9,10) (24,4) (18,16) (11,5) (12,11) (18,21) (2,13) (0,24) (10,3) (6,18) (16,1) (22,3) (19,11) (8,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph910",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,7) (0,4) (5,2) (8,6) (0,9) (5,4) (1,0) (2,0) (3,6) (0,5) (0,10) (0,3) (3,1) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph651",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (2,13) (15,8) (9,18) (14,3) (19,1) (7,4) (17,2) (2,15) (14,0) (6,9) (6,16) (19,9) (10,20) (8,11) (2,12) (10,4) (12,14) (5,9) (1,7) (2,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph294",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,5) (1,0) (12,6) (12,7) (9,11) (10,7) (14,6) (11,1) (3,13) (2,3) (4,2) (10,2) (2,11) (8,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph586",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,2) (7,18) (14,3) (0,3) (5,16) (8,5) (0,16) (2,4) (6,10) (9,4) (9,0) (14,17) (15,19) (14,18) (6,12) (1,12) (15,5) (11,5) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph498",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (8,15) (16,1) (10,5) (10,4) (0,18) (9,13) (2,17) (12,8) (11,3) (3,17) (7,10) (18,13) (6,4) (0,11) (14,1) (18,16) (4,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1142",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,9) (0,14) (0,2) (10,4) (14,12) (11,10) (7,14) (14,8) (13,10) (13,14) (3,10) (0,1) (12,6) (4,2) (0,4) (3,0) (5,12) (11,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph213",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,13) (13,2) (8,1) (2,0) (9,5) (13,3) (6,7) (4,7) (8,10) (6,8) (11,0) (2,12) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph775",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (19,22) (18,4) (2,17) (2,15) (11,3) (13,15) (11,0) (10,1) (14,9) (8,13) (22,12) (6,15) (5,1) (6,12) (12,0) (7,11) (18,1) (16,17) (0,21) (20,1) (21,9) (11,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph669",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,11) (16,1) (2,11) (3,17) (5,4) (11,19) (12,21) (8,3) (20,19) (5,18) (18,6) (2,9) (17,18) (0,15) (12,13) (11,12) (1,19) (4,10) (15,5) (21,3) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph708",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,5) (21,4) (9,17) (14,2) (16,15) (10,0) (1,19) (0,3) (1,20) (6,13) (4,2) (3,9) (9,12) (7,15) (2,19) (10,13) (15,0) (11,8) (3,18) (20,9) (8,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph654",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,12) (1,11) (19,14) (17,0) (3,7) (10,6) (15,18) (15,12) (4,2) (8,12) (6,13) (14,12) (4,9) (16,7) (2,1) (20,16) (14,0) (20,15) (4,7) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1438",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,5) (6,16) (18,2) (10,13) (11,2) (11,12) (18,7) (9,6) (14,0) (0,7) (15,4) (10,9) (4,8) (0,1) (2,10) (5,14) (4,13) (2,1) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1039",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,10) (0,3) (0,7) (9,5) (4,0) (6,0) (10,8) (4,7) (2,0) (1,5) (6,5) (8,12) (0,1) (2,9) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph488",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,6) (7,3) (17,15) (4,9) (14,15) (2,1) (16,0) (18,12) (13,6) (4,7) (7,16) (14,0) (4,2) (11,1) (12,14) (6,10) (12,8) (5,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1235",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,6) (9,15) (10,0) (14,1) (0,1) (0,13) (14,11) (3,12) (5,12) (10,2) (9,7) (8,0) (11,7) (9,10) (4,14) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1046",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,12) (1,4) (0,3) (0,1) (11,4) (8,7) (2,0) (0,6) (6,5) (12,11) (8,9) (10,2) (7,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph989",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (0,2) (11,5) (0,10) (0,1) (0,3) (10,1) (3,9) (4,7) (11,8) (4,1) (4,6) (4,8) (1,3) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph856",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,19) (10,7) (11,15) (19,18) (20,4) (0,24) (17,21) (7,12) (22,23) (11,5) (20,0) (17,13) (4,19) (22,10) (3,23) (11,9) (14,19) (22,8) (22,16) (9,23) (1,2) (5,6) (12,4) (22,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph426",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,1) (9,11) (2,8) (15,8) (8,17) (11,16) (15,11) (14,15) (8,13) (14,0) (12,3) (4,13) (7,15) (3,10) (14,5) (2,10) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph610",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,4) (11,6) (9,3) (12,17) (14,7) (10,2) (6,3) (17,20) (15,9) (8,19) (5,6) (0,8) (17,4) (20,15) (16,0) (13,19) (18,16) (1,8) (10,7) (15,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph49",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,9) (4,2) (7,8) (7,6) (8,4) (3,5) (0,6) (3,7) (4,1) (10,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph134",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,1) (1,0) (3,4) (2,1) (3,5) (10,7) (7,2) (6,9) (11,8) (12,6) (4,1) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1055",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,9) (7,3) (1,0) (0,5) (9,8) (12,8) (8,10) (3,0) (0,9) (0,2) (9,6) (4,1) (6,1) (2,11) (3,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph144",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,8) (12,2) (0,9) (0,1) (9,4) (6,11) (12,3) (1,10) (7,4) (5,2) (4,6) (6,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph727",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,15) (16,7) (5,1) (17,8) (13,12) (16,6) (2,13) (16,4) (21,22) (14,15) (8,19) (12,9) (22,17) (9,4) (8,1) (4,3) (18,6) (15,10) (3,19) (9,20) (11,18) (0,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph822",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,4) (13,1) (12,14) (6,23) (21,15) (9,4) (4,7) (14,22) (2,1) (10,6) (19,20) (15,18) (7,3) (11,22) (11,5) (7,16) (0,14) (12,15) (20,0) (16,6) (8,12) (12,17) (18,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph15",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,2) (4,8) (7,8) (0,8) (3,8) (5,2) (6,3) (9,4) (6,10) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1338",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,2) (11,4) (13,5) (15,4) (7,17) (6,3) (14,5) (9,17) (13,6) (1,10) (7,15) (8,13) (16,1) (6,0) (1,12) (7,0) (16,13) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph135",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,12) (5,1) (4,5) (2,4) (7,10) (8,1) (5,11) (12,8) (0,7) (11,3) (10,6) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph550",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,10) (5,4) (9,3) (10,1) (17,15) (18,2) (7,8) (6,9) (7,1) (14,15) (16,8) (13,0) (7,0) (1,12) (9,18) (13,19) (4,12) (11,4) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph395",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,15) (16,14) (10,9) (2,5) (6,9) (4,0) (2,1) (8,4) (0,14) (7,14) (13,7) (5,11) (12,4) (3,11) (12,11) (10,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1229",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,7) (11,0) (6,14) (4,13) (2,10) (5,8) (14,10) (0,2) (15,1) (7,2) (15,9) (0,1) (12,15) (1,3) (13,8) (0,6) (5,1) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1025",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,12) (1,0) (8,9) (1,3) (9,1) (6,7) (8,5) (0,2) (10,2) (2,7) (4,0) (4,9) (4,11) (1,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1393",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,16) (7,14) (0,15) (3,0) (4,9) (1,7) (15,6) (13,8) (4,11) (17,15) (10,15) (8,17) (17,18) (2,0) (5,17) (7,6) (0,1) (18,11) (3,18) (2,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1148",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (14,7) (9,6) (2,14) (5,3) (12,11) (9,14) (0,2) (6,10) (13,8) (4,14) (5,1) (2,3) (4,0) (4,8) (0,3) (0,6) (11,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1607",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,17) (0,8) (9,15) (0,15) (19,16) (1,8) (8,20) (5,6) (4,17) (0,1) (12,17) (18,21) (0,2) (10,2) (21,15) (3,9) (16,0) (3,6) (4,7) (7,10) (19,13) (6,11) (7,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1765",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (7,8) (20,21) (2,9) (16,0) (6,9) (13,15) (16,5) (18,13) (13,20) (7,5) (19,23) (14,20) (0,3) (11,17) (0,1) (10,3) (12,24) (2,17) (0,2) (0,10) (1,4) (8,23) (22,11) (12,15) (8,17) (2,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph93",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,3) (7,5) (2,6) (2,3) (10,0) (2,1) (5,6) (0,1) (9,11) (3,11) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1741",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,12) (6,14) (0,7) (17,9) (22,11) (23,5) (5,22) (18,23) (8,4) (21,10) (19,16) (7,1) (15,0) (9,24) (19,0) (0,4) (17,15) (21,14) (2,3) (0,1) (9,4) (0,3) (24,21) (18,10) (12,20) (0,2) (0,13) (20,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph893",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,5) (6,17) (6,19) (5,21) (2,7) (2,1) (24,22) (4,8) (15,6) (13,1) (17,9) (0,15) (20,22) (12,10) (20,15) (14,1) (14,3) (20,16) (11,4) (12,1) (13,4) (18,6) (9,11) (23,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1159",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,8) (0,5) (14,9) (4,10) (2,11) (2,0) (14,5) (10,12) (3,0) (4,1) (14,2) (10,2) (13,3) (10,6) (0,4) (3,10) (0,1) (12,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1372",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,17) (14,8) (7,5) (13,7) (16,14) (3,9) (10,13) (14,11) (10,15) (13,0) (9,16) (4,16) (14,6) (1,9) (12,17) (1,0) (7,2) (17,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1331",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,5) (6,16) (7,9) (4,11) (0,14) (8,2) (14,7) (17,7) (10,1) (1,0) (0,8) (13,11) (7,3) (3,16) (3,5) (11,15) (12,15) (17,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph33",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,8) (9,6) (4,9) (2,5) (0,1) (5,7) (0,3) (0,9) (10,7) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1125",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (3,1) (9,4) (6,7) (13,6) (8,7) (4,12) (1,0) (1,7) (1,9) (7,2) (2,0) (5,0) (4,0) (5,8) (11,2) (9,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph552",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,5) (15,11) (10,17) (18,0) (3,13) (7,8) (10,3) (7,15) (9,0) (10,1) (16,15) (16,14) (1,12) (19,0) (16,1) (4,9) (2,6) (4,6) (19,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph898",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (18,10) (19,2) (22,6) (15,17) (5,9) (17,2) (10,16) (14,19) (6,1) (24,17) (23,21) (7,13) (14,3) (15,1) (23,18) (8,15) (23,14) (7,14) (4,0) (20,12) (4,17) (15,9) (12,6) (12,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1522",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,11) (18,6) (11,9) (3,14) (2,7) (1,12) (12,10) (1,0) (16,6) (15,20) (2,1) (5,6) (0,15) (19,2) (13,4) (9,17) (8,4) (1,13) (14,1) (20,17) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph212",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,10) (0,1) (12,11) (0,8) (2,3) (7,0) (9,12) (5,0) (13,3) (5,6) (4,1) (8,10) (12,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph884",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (9,10) (2,4) (19,16) (17,3) (11,0) (16,24) (9,19) (12,20) (5,2) (20,15) (7,0) (19,13) (18,12) (4,20) (22,16) (1,12) (19,5) (8,1) (21,14) (6,17) (7,23) (6,8) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1097",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,3) (2,6) (3,8) (5,7) (0,2) (0,1) (6,11) (3,0) (9,12) (5,0) (1,8) (10,0) (1,2) (7,1) (4,0) (12,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph507",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (11,1) (0,14) (3,7) (12,8) (12,18) (11,5) (4,7) (2,4) (14,12) (4,9) (10,6) (1,2) (15,14) (6,13) (12,6) (17,15) (7,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph653",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,10) (16,17) (19,0) (19,14) (11,3) (3,7) (6,13) (16,8) (1,16) (5,10) (9,5) (4,10) (14,5) (14,15) (8,18) (20,16) (12,9) (3,14) (6,11) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph557",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,1) (14,11) (17,1) (13,16) (12,17) (5,4) (1,0) (19,14) (14,12) (2,8) (16,6) (15,4) (13,5) (9,13) (5,11) (11,8) (1,3) (15,7) (18,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1635",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (5,1) (14,15) (16,15) (12,15) (21,16) (13,22) (18,17) (6,0) (10,2) (0,2) (13,9) (7,11) (5,20) (15,10) (14,6) (7,2) (11,1) (8,19) (18,3) (4,1) (8,20) (0,1) (13,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph485",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,15) (3,9) (9,1) (13,10) (14,9) (16,4) (17,14) (7,13) (7,5) (8,18) (8,14) (2,17) (11,16) (14,6) (2,7) (10,16) (13,0) (14,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph520",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,1) (6,5) (9,18) (9,5) (1,12) (13,4) (13,1) (3,14) (4,8) (12,10) (9,11) (15,0) (7,2) (4,11) (17,2) (16,6) (6,15) (2,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph876",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (18,16) (5,13) (16,22) (1,5) (20,5) (2,9) (21,23) (16,15) (21,20) (12,16) (3,20) (4,7) (6,8) (7,15) (19,17) (19,10) (2,20) (8,20) (11,17) (0,18) (14,15) (10,21) (9,14) (9,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph330",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,8) (6,14) (2,9) (1,11) (5,6) (15,13) (6,12) (13,1) (12,4) (7,2) (5,9) (2,1) (3,14) (0,15) (10,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1259",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,10) (1,0) (9,2) (11,5) (6,14) (0,4) (2,15) (12,1) (12,6) (1,4) (11,0) (7,13) (3,11) (11,1) (0,2) (3,0) (15,0) (8,1) (13,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph183",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,2) (13,5) (5,4) (12,8) (9,0) (0,8) (7,12) (3,12) (0,10) (9,11) (13,6) (13,12) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph915",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,9) (3,1) (0,10) (0,4) (0,3) (1,0) (7,2) (5,8) (0,8) (2,0) (2,3) (6,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1111",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,2) (8,7) (11,13) (13,4) (1,13) (0,1) (8,10) (4,0) (12,3) (7,6) (12,6) (9,0) (6,5) (4,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph816",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (10,2) (1,17) (20,10) (20,12) (22,0) (19,11) (17,9) (19,2) (18,6) (3,7) (15,5) (14,16) (6,21) (8,18) (9,15) (16,13) (7,17) (23,6) (3,11) (4,0) (13,22) (8,20) (18,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1501",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,11) (17,8) (14,6) (9,19) (0,13) (11,2) (0,11) (5,0) (4,0) (3,20) (18,5) (4,8) (10,12) (1,6) (0,15) (6,7) (12,7) (2,0) (3,0) (12,18) (9,2) (0,1) (20,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1686",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,1) (0,1) (5,11) (16,6) (6,18) (20,0) (16,7) (17,12) (9,4) (2,4) (2,0) (18,15) (12,15) (11,22) (14,22) (21,15) (6,10) (13,1) (4,7) (3,7) (6,23) (3,0) (14,12) (12,8) (0,14) (20,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1482",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,5) (4,2) (5,16) (17,14) (8,5) (6,12) (1,0) (14,18) (2,13) (16,0) (4,9) (6,5) (3,14) (5,15) (0,3) (6,10) (12,1) (19,15) (18,7) (0,2) (9,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph734",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (21,8) (20,17) (6,12) (13,17) (9,15) (18,7) (8,1) (6,10) (21,19) (3,6) (5,15) (0,15) (16,20) (4,17) (22,5) (7,4) (19,14) (9,3) (7,11) (0,16) (0,8) (10,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1407",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,9) (13,10) (16,11) (12,11) (9,14) (8,18) (3,8) (0,4) (6,7) (15,4) (5,16) (3,2) (3,16) (8,4) (1,16) (13,17) (5,0) (8,10) (3,0) (2,0) (12,6) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph518",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,11) (12,15) (3,1) (10,8) (13,8) (14,0) (9,7) (13,7) (17,18) (17,14) (6,18) (11,15) (5,17) (16,3) (10,14) (3,4) (2,16) (1,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph897",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (8,22) (22,3) (2,21) (5,0) (16,10) (23,24) (15,13) (20,17) (6,7) (20,6) (11,10) (21,24) (3,1) (8,14) (19,5) (15,18) (10,3) (8,6) (5,15) (7,12) (9,14) (4,14) (21,16) (9,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph366",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,14) (16,12) (2,11) (2,5) (4,13) (14,11) (13,7) (13,9) (1,0) (10,6) (1,3) (5,3) (16,13) (8,14) (10,15) (10,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1156",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,4) (9,13) (0,2) (7,2) (3,13) (1,13) (2,3) (12,13) (14,13) (10,3) (3,0) (8,11) (5,8) (8,6) (0,1) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph210",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,8) (12,4) (3,11) (8,0) (8,7) (8,3) (8,10) (11,6) (1,5) (13,12) (11,12) (5,2) (4,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph450",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,17) (2,15) (0,10) (14,5) (12,5) (8,4) (16,1) (9,0) (1,12) (14,3) (8,7) (11,16) (6,11) (5,4) (2,10) (13,14) (10,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph45",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,6) (1,10) (2,6) (7,3) (4,7) (5,9) (5,6) (8,1) (2,0) (2,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1340",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,1) (3,13) (9,16) (10,8) (14,17) (3,2) (15,5) (1,0) (8,6) (1,6) (13,11) (13,8) (4,14) (0,2) (7,13) (15,12) (14,5) (1,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph671",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,20) (12,2) (5,10) (13,0) (20,0) (4,17) (14,10) (5,19) (11,15) (5,3) (10,6) (2,11) (6,7) (17,15) (18,11) (9,8) (12,14) (21,16) (15,1) (16,0) (10,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph235",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,6) (6,8) (9,0) (7,4) (10,13) (13,2) (1,0) (3,12) (5,8) (6,4) (9,4) (2,5) (1,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1164",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,0) (1,4) (12,5) (7,10) (3,4) (6,4) (11,7) (5,14) (14,0) (0,2) (8,9) (2,4) (0,1) (7,14) (9,2) (3,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1180",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,3) (14,8) (14,3) (8,12) (13,1) (9,8) (6,11) (6,13) (8,2) (0,1) (0,5) (0,7) (10,4) (2,0) (3,0) (10,7) (12,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1729",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,6) (0,5) (4,0) (17,1) (6,23) (6,16) (6,1) (18,3) (18,9) (19,14) (6,4) (19,13) (6,5) (9,13) (8,22) (23,7) (8,14) (0,15) (0,1) (2,0) (3,0) (11,9) (18,2) (12,11) (20,14) (21,12) (20,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph716",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (5,19) (2,21) (6,9) (4,5) (18,2) (13,0) (1,7) (14,15) (10,14) (12,4) (4,11) (8,16) (20,7) (3,9) (7,8) (15,17) (18,9) (12,1) (21,13) (20,0) (10,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph394",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,1) (15,3) (9,0) (15,14) (10,3) (0,11) (10,16) (2,0) (6,4) (6,11) (13,5) (7,1) (11,8) (0,1) (8,13) (14,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1221",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,11) (3,4) (6,13) (10,12) (3,0) (15,14) (4,13) (5,2) (0,2) (10,2) (7,11) (0,4) (1,8) (14,5) (2,8) (5,0) (1,0) (9,10) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1258",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,13) (2,1) (1,0) (6,10) (11,1) (9,8) (10,12) (0,3) (11,5) (13,0) (12,11) (14,12) (12,15) (0,5) (7,4) (15,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph799",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (20,10) (8,15) (13,21) (2,8) (23,15) (22,23) (14,6) (18,4) (5,13) (21,17) (21,8) (21,12) (22,3) (3,11) (9,16) (22,18) (14,0) (7,1) (1,23) (21,16) (15,14) (2,10) (11,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph132",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,5) (4,2) (7,12) (6,11) (11,3) (9,1) (0,7) (11,10) (8,10) (0,8) (5,4) (11,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1497",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,13) (4,1) (2,17) (11,13) (19,3) (4,5) (15,4) (6,19) (1,0) (6,17) (8,5) (10,14) (0,3) (6,18) (6,14) (4,19) (12,5) (16,12) (7,4) (9,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph792",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,18) (13,14) (10,2) (0,14) (0,1) (8,0) (10,5) (9,23) (3,16) (15,23) (7,23) (11,16) (12,3) (23,6) (6,22) (21,16) (13,3) (20,17) (17,4) (19,9) (12,20) (18,0) (22,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1519",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,11) (12,8) (20,16) (20,15) (14,12) (16,7) (7,3) (0,1) (12,6) (15,18) (10,6) (2,4) (0,2) (14,0) (17,0) (7,4) (14,19) (6,13) (1,2) (15,12) (9,4) (5,11) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph640",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (5,15) (2,3) (0,6) (11,13) (15,8) (20,1) (8,9) (2,11) (17,2) (10,9) (18,14) (14,16) (4,1) (7,18) (6,18) (19,15) (20,12) (9,18) (4,17) (8,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph196",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,12) (10,6) (12,3) (11,2) (3,10) (9,13) (4,7) (2,0) (11,7) (4,8) (6,1) (12,13) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph20",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,3) (5,6) (7,2) (8,4) (6,3) (0,9) (7,3) (6,0) (1,5) (10,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph303",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,2) (12,14) (0,15) (9,11) (6,4) (7,10) (15,10) (1,15) (8,0) (10,14) (11,13) (3,5) (6,9) (5,10) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1064",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,11) (0,3) (6,1) (2,0) (2,11) (6,10) (7,10) (6,5) (12,3) (3,9) (4,8) (7,12) (0,1) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1356",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,5) (16,10) (16,17) (11,6) (2,0) (3,14) (4,9) (2,17) (3,5) (12,16) (6,5) (9,14) (13,15) (3,0) (0,14) (14,8) (14,7) (1,0) (1,17) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1646",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (6,1) (20,15) (20,9) (11,2) (6,7) (14,0) (3,8) (0,4) (0,1) (8,21) (18,22) (19,5) (11,17) (9,21) (0,2) (0,11) (22,0) (12,18) (3,0) (13,6) (2,21) (12,7) (5,0) (4,12) (8,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph833",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,11) (8,4) (6,3) (11,2) (13,21) (0,2) (14,4) (23,14) (8,21) (19,7) (22,1) (20,1) (9,23) (1,15) (19,9) (1,12) (3,10) (10,17) (16,7) (20,17) (18,23) (17,16) (5,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph392",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,1) (4,13) (16,9) (14,9) (3,15) (2,15) (0,3) (0,10) (10,11) (7,2) (9,8) (6,8) (5,15) (2,12) (9,3) (13,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph735",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (6,2) (21,15) (12,0) (3,10) (18,16) (7,9) (6,4) (1,16) (4,9) (10,1) (11,19) (15,11) (1,13) (22,17) (15,7) (0,17) (10,20) (16,22) (22,8) (3,14) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph442",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,7) (9,1) (4,10) (17,3) (8,4) (15,1) (15,0) (17,7) (5,3) (2,0) (12,7) (14,4) (12,6) (13,4) (3,11) (16,1) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1654",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (2,12) (18,9) (2,0) (15,13) (0,4) (22,10) (3,20) (14,8) (1,9) (16,6) (21,6) (3,18) (3,13) (6,0) (8,1) (21,18) (16,19) (0,1) (11,15) (18,17) (10,19) (7,20) (9,5) (1,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph370",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,3) (12,5) (7,4) (2,7) (5,13) (4,6) (9,0) (8,7) (5,10) (1,16) (1,8) (1,13) (11,2) (10,15) (3,11) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1059",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,10) (8,7) (1,11) (0,3) (5,12) (10,5) (0,4) (9,0) (2,4) (7,2) (6,3) (2,0) (2,11) (9,1) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1385",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,9) (16,2) (13,15) (18,0) (9,17) (3,11) (18,4) (0,11) (1,12) (12,6) (5,1) (10,1) (15,2) (17,0) (11,1) (2,0) (11,7) (15,6) (8,13) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph244",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,8) (1,9) (5,9) (11,13) (4,0) (12,13) (14,12) (1,2) (7,2) (1,0) (14,10) (10,3) (14,5) (6,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1320",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,4) (12,15) (8,0) (0,3) (12,1) (0,2) (8,10) (2,13) (8,17) (17,6) (16,11) (3,16) (4,0) (0,1) (13,1) (12,14) (10,9) (0,13) (5,2) (14,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph242",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,6) (11,3) (2,1) (3,8) (1,7) (9,12) (10,0) (0,4) (5,7) (1,8) (14,11) (2,6) (2,0) (13,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1337",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,5) (4,13) (1,0) (2,9) (15,6) (13,1) (2,0) (12,10) (0,15) (12,1) (2,7) (5,6) (1,14) (1,2) (8,4) (11,4) (17,11) (3,14) (6,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1113",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,1) (13,3) (6,9) (5,1) (13,8) (1,12) (2,0) (2,13) (11,4) (2,4) (12,3) (0,13) (0,3) (5,10) (9,1) (7,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1411",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,5) (15,12) (1,9) (10,8) (5,18) (13,8) (0,4) (13,11) (3,0) (5,15) (5,1) (13,7) (1,0) (2,0) (9,16) (13,3) (6,1) (6,8) (14,17) (2,3) (4,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph380",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,11) (2,8) (7,11) (9,6) (2,4) (12,13) (3,14) (14,7) (0,1) (2,11) (11,5) (3,1) (0,13) (16,9) (12,15) (2,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1627",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,21) (1,21) (16,10) (4,7) (10,4) (20,13) (21,2) (0,5) (1,0) (3,2) (11,20) (18,17) (22,6) (5,19) (13,6) (18,15) (10,15) (8,9) (14,18) (13,14) (13,0) (3,4) (3,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1185",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,3) (8,9) (13,1) (6,11) (2,8) (0,2) (10,4) (13,6) (0,1) (5,0) (14,8) (4,12) (3,0) (3,11) (10,7) (8,12) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph84",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,11) (11,0) (6,3) (3,9) (9,1) (7,8) (6,11) (7,2) (1,8) (11,4) (9,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1540",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,19) (6,13) (14,15) (5,10) (5,14) (12,9) (11,6) (1,16) (16,8) (3,2) (4,10) (1,0) (11,3) (19,0) (17,16) (7,3) (10,8) (18,8) (20,16) (5,9) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1580",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,16) (4,18) (11,15) (3,15) (10,11) (2,11) (6,0) (5,13) (2,4) (12,19) (5,9) (0,3) (5,14) (8,14) (0,4) (7,17) (7,15) (4,1) (11,21) (15,13) (2,0) (3,6) (0,19) (9,20) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph707",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,12) (21,19) (13,3) (1,9) (6,16) (18,3) (1,11) (13,14) (16,19) (4,0) (3,17) (9,18) (15,18) (9,5) (7,20) (18,21) (8,1) (6,20) (15,10) (12,2) (6,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1671",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,20) (21,22) (9,5) (13,12) (0,7) (14,22) (10,16) (16,8) (2,0) (2,13) (20,21) (18,8) (17,15) (12,7) (21,17) (5,22) (9,4) (4,0) (6,11) (3,19) (0,1) (3,0) (11,9) (5,0) (13,8) (1,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1677",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (19,5) (2,4) (5,6) (13,16) (6,12) (17,22) (14,0) (2,0) (17,1) (2,17) (16,15) (3,0) (16,10) (21,20) (14,8) (14,9) (20,15) (11,18) (4,9) (1,0) (7,14) (22,20) (5,3) (18,19) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph258",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,11) (0,2) (10,9) (7,1) (12,3) (2,10) (14,7) (9,7) (5,9) (0,4) (4,12) (1,8) (0,13) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph581",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,0) (12,7) (12,18) (12,10) (6,14) (2,11) (13,0) (4,8) (9,18) (6,1) (7,6) (0,3) (16,8) (15,0) (2,9) (11,8) (3,19) (0,5) (17,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph339",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,4) (6,5) (15,9) (10,2) (0,4) (12,7) (10,7) (0,15) (8,1) (6,3) (6,11) (8,0) (3,9) (15,14) (8,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph236",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,7) (5,6) (6,8) (2,7) (2,11) (10,11) (7,1) (0,2) (12,4) (12,13) (11,5) (12,8) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1596",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,0) (14,3) (5,9) (0,15) (14,1) (6,17) (9,17) (5,19) (11,4) (4,8) (16,6) (15,20) (0,3) (9,11) (2,0) (13,1) (6,21) (6,18) (20,2) (7,2) (1,12) (1,2) (13,4) (10,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1577",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,16) (0,3) (2,0) (21,19) (3,17) (18,13) (0,4) (7,12) (2,13) (11,9) (6,11) (0,1) (8,16) (16,10) (9,5) (0,7) (12,21) (10,20) (8,15) (13,8) (14,21) (12,20) (9,4) (17,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph427",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,5) (9,3) (1,8) (15,0) (6,2) (7,5) (2,9) (6,4) (10,8) (7,16) (8,2) (17,13) (17,15) (8,11) (11,12) (14,10) (7,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1469",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,19) (14,8) (10,16) (17,2) (1,0) (0,2) (2,4) (5,18) (3,5) (14,7) (15,16) (3,0) (9,4) (15,19) (0,14) (9,14) (14,3) (13,16) (12,6) (11,18) (17,1) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph945",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (3,0) (5,0) (1,2) (2,3) (8,4) (9,7) (5,9) (0,4) (6,2) (10,2) (10,7) (3,8) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1262",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,15) (6,1) (7,3) (16,1) (0,1) (10,2) (8,6) (13,7) (0,2) (5,15) (2,11) (6,0) (12,16) (9,14) (10,8) (0,4) (13,9) (3,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph645",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,12) (3,4) (2,5) (0,19) (9,13) (18,13) (13,11) (10,15) (6,13) (8,17) (14,9) (11,20) (9,5) (15,19) (0,17) (13,0) (17,1) (3,8) (7,0) (16,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph417",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,7) (8,5) (15,10) (12,15) (16,7) (15,14) (10,2) (3,1) (1,16) (13,4) (1,5) (9,15) (6,14) (0,11) (13,8) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph270",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,2) (0,1) (11,8) (5,14) (2,13) (12,3) (1,12) (10,5) (4,9) (7,9) (13,11) (13,6) (2,4) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph545",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,18) (17,9) (10,12) (2,1) (15,0) (17,19) (15,6) (1,13) (5,6) (11,9) (1,14) (5,9) (13,4) (3,14) (11,4) (7,2) (12,1) (16,6) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1798",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,24) (19,7) (1,6) (11,8) (21,0) (13,4) (5,2) (17,10) (0,3) (17,23) (12,13) (18,14) (22,16) (18,21) (11,17) (15,13) (17,14) (3,5) (0,1) (4,14) (2,0) (9,10) (13,20) (16,10) (14,19) (3,1) (2,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1313",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,1) (10,11) (14,9) (8,6) (2,16) (3,4) (1,6) (11,7) (12,7) (14,7) (5,10) (0,2) (7,6) (0,3) (14,13) (3,13) (15,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph247",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,10) (6,12) (12,7) (11,1) (11,2) (6,14) (3,2) (1,0) (3,13) (4,2) (2,10) (9,11) (5,8) (8,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1077",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,2) (2,12) (1,0) (2,8) (4,7) (1,3) (0,3) (7,3) (0,2) (4,0) (0,9) (11,8) (2,6) (9,1) (5,10) (10,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1756",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,24) (20,15) (19,8) (13,5) (0,1) (8,1) (7,1) (18,6) (4,9) (18,11) (8,17) (15,13) (10,16) (24,2) (3,19) (17,22) (12,0) (16,4) (9,21) (11,15) (23,3) (16,6) (24,22) (12,9) (12,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1553",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,12) (11,8) (2,8) (12,13) (6,13) (20,16) (11,14) (12,3) (17,7) (5,7) (12,1) (12,7) (17,4) (1,19) (1,0) (19,18) (0,11) (17,10) (9,11) (5,16) (0,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1195",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,11) (7,13) (14,7) (8,9) (4,7) (14,10) (2,0) (3,0) (2,9) (8,10) (3,6) (6,12) (1,7) (4,0) (0,1) (12,10) (5,0) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph907",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,7) (9,2) (7,3) (5,9) (3,6) (4,1) (2,0) (5,1) (0,1) (3,8) (0,3) (10,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph765",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (19,12) (3,6) (14,15) (13,10) (7,2) (9,2) (17,13) (1,22) (15,17) (6,4) (20,17) (2,11) (21,16) (16,12) (11,21) (5,9) (4,9) (12,18) (8,5) (0,2) (20,1) (10,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1448",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,0) (15,11) (17,2) (0,5) (0,1) (5,7) (2,18) (10,3) (17,11) (2,9) (0,4) (16,8) (13,14) (13,18) (8,7) (19,13) (4,1) (3,0) (2,0) (9,6) (5,12) (17,8) (16,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph490",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,5) (9,4) (13,15) (10,12) (4,16) (14,11) (16,6) (8,15) (9,17) (6,15) (11,18) (9,12) (16,7) (0,12) (3,18) (3,4) (1,8) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1659",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,3) (13,9) (12,18) (5,0) (19,16) (15,9) (11,19) (12,21) (19,6) (5,16) (11,12) (0,20) (4,18) (7,14) (10,15) (0,8) (10,17) (1,0) (0,3) (1,2) (13,20) (1,11) (3,12) (2,0) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1276",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,2) (7,12) (3,4) (9,14) (13,14) (7,14) (6,8) (0,3) (13,3) (10,11) (7,11) (15,12) (1,6) (6,7) (10,5) (1,0) (16,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph18",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,2) (8,7) (10,8) (5,10) (0,2) (9,3) (7,3) (4,7) (6,4) (6,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1309",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,7) (0,3) (9,13) (6,8) (14,9) (12,14) (8,7) (10,9) (2,11) (5,8) (16,1) (8,3) (3,12) (15,12) (2,14) (0,1) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1377",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,15) (1,9) (0,4) (6,4) (12,13) (14,8) (16,2) (10,17) (4,3) (12,7) (9,4) (14,3) (0,2) (0,3) (10,11) (12,2) (6,13) (10,16) (0,1) (5,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph416",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,13) (7,5) (2,8) (5,16) (1,12) (10,11) (16,15) (9,12) (8,11) (14,1) (7,13) (12,3) (12,7) (6,11) (12,0) (0,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph509",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,17) (4,7) (7,18) (14,5) (12,10) (17,12) (0,6) (18,13) (15,7) (13,14) (9,7) (14,17) (18,16) (1,3) (18,8) (6,3) (2,10) (11,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph470",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,12) (3,14) (9,4) (6,11) (5,17) (14,15) (5,7) (14,13) (5,16) (1,12) (8,6) (5,6) (2,4) (10,5) (0,9) (16,0) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1014",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,0) (8,1) (3,9) (3,2) (0,1) (2,7) (8,6) (5,8) (3,0) (4,0) (8,3) (4,10) (8,11) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph914",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (7,3) (4,6) (2,7) (0,3) (0,2) (7,5) (10,6) (4,8) (1,0) (0,4) (1,5) (7,0) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1223",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,0) (11,3) (15,0) (0,1) (0,4) (0,3) (5,2) (1,2) (12,4) (7,13) (9,6) (10,7) (0,14) (11,12) (10,9) (4,8) (11,5) (7,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph675",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (14,15) (12,1) (16,8) (20,0) (21,2) (10,1) (7,8) (9,3) (7,20) (7,1) (4,12) (21,13) (5,19) (11,4) (18,9) (5,4) (18,2) (6,9) (17,15) (14,10) (13,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1314",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,13) (16,2) (11,3) (3,10) (0,1) (10,9) (14,16) (6,8) (8,12) (8,0) (11,0) (15,2) (12,2) (5,3) (4,1) (10,7) (2,0) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph174",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,1) (3,11) (10,5) (8,6) (4,12) (6,11) (7,8) (0,7) (2,0) (8,10) (9,4) (3,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph9",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,1) (9,7) (7,6) (0,5) (10,8) (8,3) (4,5) (8,4) (5,9) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph692",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,16) (20,0) (8,13) (4,2) (21,4) (5,1) (6,15) (13,2) (11,0) (12,9) (6,14) (11,18) (5,16) (13,3) (16,19) (0,7) (15,9) (20,10) (16,7) (5,17) (13,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1170",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,0) (1,11) (2,0) (12,13) (0,4) (4,9) (4,7) (3,10) (7,2) (0,3) (4,5) (8,5) (3,1) (10,0) (1,4) (11,6) (4,14) (8,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1408",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,16) (7,1) (2,0) (13,5) (9,18) (3,15) (2,14) (14,15) (10,18) (3,10) (4,6) (1,0) (8,11) (17,8) (6,11) (13,17) (11,0) (3,0) (12,0) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1710",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,2) (2,20) (12,23) (16,21) (4,9) (19,22) (23,9) (19,1) (3,14) (20,9) (7,21) (7,1) (21,23) (6,17) (8,15) (5,8) (0,1) (11,2) (9,6) (2,18) (14,0) (21,10) (14,2) (12,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph712",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (19,15) (8,6) (7,13) (13,15) (8,10) (3,13) (1,5) (6,20) (9,1) (14,4) (20,9) (19,5) (2,3) (18,21) (19,11) (13,12) (0,2) (8,16) (21,14) (17,1) (14,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1332",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,17) (11,0) (7,13) (6,12) (3,11) (1,8) (15,10) (3,0) (5,11) (0,16) (12,1) (14,2) (15,2) (4,1) (11,1) (6,15) (1,0) (0,4) (0,2) (9,13) (0,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph230",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,5) (8,0) (6,0) (0,7) (11,13) (6,5) (13,10) (12,10) (13,3) (5,1) (4,7) (2,9) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph77",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,2) (9,3) (1,10) (11,5) (4,2) (5,6) (1,0) (6,2) (11,7) (9,5) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1104",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,11) (0,1) (2,8) (1,12) (5,10) (6,12) (4,0) (0,3) (12,11) (7,2) (5,9) (7,1) (7,13) (11,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1087",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,3) (7,0) (10,1) (4,3) (10,5) (11,2) (6,1) (0,2) (13,11) (0,11) (11,10) (0,1) (2,3) (8,4) (1,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph921",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,9) (6,7) (7,4) (2,0) (9,1) (0,3) (6,3) (0,1) (0,7) (0,4) (3,9) (4,10) (1,5) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1471",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (4,0) (2,0) (10,5) (0,1) (18,6) (4,17) (6,11) (0,18) (12,9) (9,10) (16,3) (12,3) (3,0) (14,13) (6,17) (16,2) (15,16) (2,8) (0,7) (11,19) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1670",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (9,5) (0,4) (2,16) (11,6) (6,15) (0,2) (0,3) (19,1) (4,3) (18,16) (16,19) (20,8) (14,5) (3,14) (11,3) (0,22) (13,9) (14,17) (21,14) (3,12) (10,5) (7,10) (19,0) (10,8) (1,0) (16,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1045",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,11) (10,6) (4,7) (0,3) (7,12) (12,11) (0,2) (1,0) (12,3) (6,1) (7,10) (5,6) (8,4) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1231",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,8) (8,10) (0,5) (1,0) (11,4) (5,9) (5,8) (2,0) (9,6) (9,2) (10,12) (14,13) (3,0) (15,12) (7,0) (1,13) (11,3) (0,4) (12,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph412",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,9) (2,11) (15,0) (10,12) (16,3) (5,4) (8,2) (1,5) (3,13) (6,11) (7,3) (15,11) (3,12) (1,3) (14,5) (12,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1783",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (16,15) (20,16) (21,3) (14,4) (21,0) (19,5) (2,0) (11,18) (8,23) (24,4) (14,11) (17,1) (12,23) (16,3) (14,21) (9,12) (13,23) (2,19) (2,6) (0,1) (14,13) (10,20) (22,19) (19,9) (1,20) (7,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph431",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,17) (17,16) (14,0) (1,17) (13,7) (11,5) (8,12) (11,14) (10,8) (13,17) (3,4) (15,9) (16,2) (1,3) (3,15) (6,7) (14,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph21",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,5) (8,4) (6,5) (10,4) (7,2) (3,4) (6,0) (0,9) (6,3) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1168",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,10) (1,0) (11,4) (14,0) (7,14) (11,6) (13,10) (3,5) (13,0) (11,9) (3,1) (6,14) (1,4) (4,12) (13,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1202",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,9) (6,5) (14,7) (1,8) (2,7) (9,11) (2,15) (13,15) (3,0) (12,4) (7,10) (3,14) (0,2) (9,6) (0,1) (12,9) (11,0) (13,1) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1197",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,8) (7,8) (6,5) (4,14) (11,9) (4,1) (14,2) (0,6) (2,12) (0,1) (11,5) (7,13) (14,0) (0,3) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1132",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,12) (9,13) (0,2) (0,8) (11,10) (0,3) (1,0) (9,1) (2,10) (1,4) (10,5) (10,13) (0,10) (7,11) (9,3) (4,0) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1311",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,5) (9,6) (9,2) (0,3) (8,11) (16,13) (0,10) (3,10) (13,2) (2,0) (7,8) (15,11) (14,13) (5,7) (0,16) (0,1) (8,2) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph354",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,11) (10,12) (14,12) (15,10) (9,4) (7,5) (3,4) (5,9) (1,6) (12,13) (8,2) (0,2) (12,11) (9,15) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph385",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,13) (1,5) (9,10) (11,5) (2,15) (5,8) (12,5) (8,14) (4,9) (6,9) (16,7) (13,1) (16,4) (3,15) (0,4) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph722",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,2) (19,1) (17,0) (22,6) (22,18) (0,11) (16,18) (1,12) (8,13) (17,12) (11,10) (9,11) (4,17) (13,17) (20,7) (7,5) (16,5) (7,12) (11,15) (21,19) (14,12) (3,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1409",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,17) (18,11) (14,3) (1,8) (1,5) (11,15) (7,15) (0,1) (6,2) (4,16) (13,0) (14,12) (1,11) (10,11) (6,16) (16,9) (14,5) (4,8) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph971",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,8) (0,1) (1,2) (0,3) (6,2) (4,3) (11,0) (9,8) (2,0) (6,5) (10,1) (3,6) (8,11) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1508",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,4) (8,0) (13,6) (11,18) (15,16) (3,17) (0,10) (11,10) (8,9) (12,1) (0,3) (7,2) (17,19) (3,20) (13,17) (15,6) (8,15) (18,5) (18,4) (1,0) (15,2) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1243",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,13) (5,3) (5,10) (14,10) (15,1) (12,2) (8,0) (0,2) (6,4) (0,15) (1,0) (3,0) (6,9) (7,10) (4,0) (14,12) (15,10) (11,2) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph193",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,7) (10,12) (13,12) (5,3) (1,8) (3,9) (4,9) (11,13) (7,12) (13,6) (11,2) (1,5) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph325",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,3) (3,6) (8,11) (2,0) (6,13) (6,1) (10,4) (8,2) (8,12) (5,4) (12,15) (9,0) (0,4) (14,1) (15,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph404",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,14) (0,6) (16,12) (0,2) (6,9) (4,11) (10,8) (7,0) (4,2) (6,8) (14,13) (1,15) (13,15) (5,3) (3,12) (12,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1649",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,22) (15,22) (0,16) (4,18) (6,2) (5,14) (0,11) (16,12) (1,0) (19,4) (20,9) (12,1) (6,10) (19,5) (17,14) (3,22) (21,4) (20,7) (7,3) (10,21) (10,0) (0,2) (8,5) (14,13) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph116",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,0) (0,7) (8,4) (8,5) (10,3) (10,2) (6,3) (1,8) (4,11) (6,5) (1,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph807",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,20) (8,0) (2,22) (23,9) (17,4) (6,18) (16,3) (12,20) (12,3) (22,6) (2,10) (13,14) (23,7) (9,19) (18,0) (11,16) (23,15) (23,6) (16,21) (10,5) (3,13) (0,1) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph175",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (6,11) (9,7) (7,6) (9,12) (6,3) (8,6) (5,7) (10,4) (12,1) (1,2) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph126",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,5) (11,0) (2,8) (12,3) (10,11) (1,7) (5,4) (3,7) (5,8) (4,9) (0,12) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph553",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (12,16) (6,15) (0,12) (2,4) (1,12) (7,5) (17,16) (17,2) (15,18) (7,4) (2,19) (7,11) (8,14) (13,19) (12,8) (5,10) (19,9) (3,6) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph881",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (24,6) (11,1) (17,7) (23,20) (1,21) (14,7) (3,13) (4,7) (4,9) (16,24) (21,23) (12,8) (0,2) (12,4) (22,15) (19,4) (10,21) (18,4) (4,1) (3,17) (15,0) (5,3) (24,17) (22,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph567",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,14) (12,19) (10,14) (8,7) (14,13) (8,14) (5,2) (0,2) (6,18) (15,11) (1,18) (17,11) (14,9) (6,7) (5,3) (4,12) (6,15) (12,6) (16,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph443",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,10) (10,3) (8,17) (5,16) (10,0) (11,7) (6,17) (16,1) (14,4) (15,12) (7,17) (12,13) (0,15) (9,11) (2,14) (0,14) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1124",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,10) (7,6) (0,3) (4,13) (4,5) (12,0) (0,1) (6,5) (1,9) (11,9) (3,7) (0,4) (10,11) (3,2) (3,8) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph561",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,7) (8,0) (4,13) (16,6) (10,5) (0,9) (5,4) (13,17) (9,3) (1,8) (0,18) (2,15) (7,11) (12,4) (14,7) (8,19) (9,6) (17,2) (4,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph279",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,6) (14,5) (11,12) (2,4) (7,11) (13,9) (1,4) (13,14) (2,3) (4,8) (5,1) (10,1) (2,11) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1764",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,12) (9,5) (24,21) (20,10) (2,13) (10,16) (13,23) (16,1) (16,8) (24,5) (8,19) (20,21) (8,13) (17,18) (4,9) (0,1) (7,0) (3,0) (22,15) (3,22) (11,6) (17,21) (7,12) (22,14) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph379",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,16) (3,1) (8,11) (15,7) (0,14) (1,0) (9,13) (8,2) (5,13) (11,5) (11,14) (13,15) (12,4) (5,4) (6,16) (10,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph187",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,13) (3,11) (6,11) (1,5) (11,12) (8,2) (2,5) (12,4) (8,10) (8,3) (9,4) (8,7) (0,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph920",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,1) (5,6) (7,2) (8,6) (0,2) (1,8) (0,3) (7,3) (9,5) (2,6) (7,4) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph83",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,5) (11,2) (7,6) (9,8) (7,3) (7,0) (2,0) (1,8) (10,2) (6,8) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1699",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (21,4) (14,12) (6,13) (7,0) (1,0) (13,15) (17,8) (3,15) (10,9) (8,7) (10,21) (16,22) (7,11) (7,19) (22,23) (11,1) (4,23) (9,0) (2,15) (9,5) (13,21) (20,18) (0,14) (20,9) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1441",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,0) (0,18) (1,0) (15,8) (0,13) (4,3) (11,9) (3,8) (5,2) (13,19) (11,12) (8,17) (17,1) (14,19) (17,13) (16,0) (9,13) (13,6) (15,10) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1563",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (5,12) (4,9) (1,15) (0,2) (2,13) (14,8) (7,15) (0,20) (10,8) (0,1) (20,2) (0,3) (2,6) (17,10) (11,12) (18,21) (20,18) (6,9) (4,0) (7,5) (16,17) (15,2) (3,8) (8,11) (7,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1608",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,2) (3,11) (0,2) (17,9) (19,8) (14,16) (13,7) (6,20) (21,18) (2,10) (4,0) (18,8) (9,15) (12,20) (10,20) (0,18) (16,13) (0,1) (15,5) (7,3) (19,11) (1,17) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph524",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,15) (3,16) (1,16) (0,1) (8,18) (8,3) (2,3) (11,16) (6,7) (12,6) (10,13) (8,10) (16,5) (4,8) (11,12) (9,14) (18,9) (13,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph233",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,0) (12,0) (9,3) (5,8) (11,0) (12,10) (3,0) (2,13) (1,3) (6,11) (2,8) (10,2) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1757",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (1,9) (2,20) (12,9) (14,19) (21,11) (22,5) (3,23) (17,3) (11,23) (24,23) (8,17) (4,0) (22,2) (9,8) (1,0) (2,0) (15,5) (6,13) (14,16) (23,13) (10,7) (18,15) (7,14) (13,5) (16,4) (22,4) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph329",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,13) (0,10) (9,3) (15,2) (3,11) (13,12) (4,12) (2,1) (8,2) (5,4) (6,1) (13,14) (1,7) (11,6) (10,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1567",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,18) (0,4) (9,18) (16,6) (5,9) (21,19) (6,0) (17,3) (16,19) (20,7) (11,1) (1,9) (15,18) (14,13) (2,12) (20,6) (3,13) (0,2) (8,1) (1,0) (8,12) (10,15) (18,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph753",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,1) (12,14) (11,2) (4,6) (4,7) (9,0) (18,11) (7,2) (5,19) (20,13) (22,21) (13,22) (10,19) (16,3) (19,0) (22,15) (8,7) (1,10) (14,5) (17,21) (3,20) (5,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph301",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,1) (4,0) (10,7) (7,14) (14,0) (4,8) (0,15) (9,6) (11,12) (10,9) (11,3) (2,5) (5,11) (4,12) (13,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph986",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,7) (2,11) (1,6) (10,8) (3,4) (4,5) (8,9) (10,11) (2,0) (1,0) (5,6) (2,4) (8,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1101",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,2) (11,1) (13,10) (12,5) (7,12) (5,13) (12,6) (2,8) (1,13) (0,3) (11,0) (10,4) (1,0) (2,0) (3,10) (9,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1434",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,0) (10,16) (6,11) (0,4) (15,2) (12,13) (0,2) (0,3) (18,15) (14,7) (13,0) (9,8) (1,3) (7,11) (2,11) (0,1) (12,17) (14,3) (17,4) (11,16) (5,2) (2,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph241",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,14) (9,5) (9,3) (11,13) (10,4) (1,8) (14,12) (4,2) (7,13) (8,6) (1,12) (5,1) (0,13) (13,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1775",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,10) (20,22) (15,7) (0,14) (11,23) (7,21) (20,13) (14,24) (7,12) (1,20) (0,16) (5,1) (17,3) (17,12) (8,11) (18,24) (15,11) (16,19) (18,3) (2,0) (0,1) (6,23) (3,5) (8,4) (9,22) (19,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph894",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,0) (10,13) (4,24) (16,20) (17,6) (20,12) (5,16) (15,16) (3,13) (13,18) (8,22) (4,2) (18,11) (5,1) (0,21) (19,5) (7,23) (15,9) (16,7) (0,11) (2,13) (9,14) (7,24) (6,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph596",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,3) (13,16) (17,1) (11,8) (6,16) (2,8) (18,0) (10,1) (15,7) (1,0) (13,5) (9,13) (19,14) (11,14) (14,12) (4,5) (4,15) (11,5) (12,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph327",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,2) (3,10) (14,11) (2,13) (7,5) (13,12) (8,2) (1,0) (9,6) (7,8) (13,15) (1,4) (10,0) (8,11) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph147",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,6) (2,12) (7,9) (1,4) (3,11) (12,8) (4,0) (1,12) (10,2) (0,9) (5,8) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph316",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,1) (14,6) (0,6) (2,6) (5,1) (9,13) (8,12) (10,11) (8,14) (9,3) (7,12) (13,14) (3,15) (6,4) (11,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph346",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,9) (4,5) (12,3) (1,14) (13,0) (15,9) (4,14) (7,11) (6,15) (10,2) (9,10) (12,5) (11,14) (10,0) (0,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph35",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (1,3) (3,2) (7,2) (9,10) (6,0) (4,0) (8,0) (8,5) (0,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1773",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,9) (3,8) (0,7) (0,19) (24,4) (7,15) (23,4) (0,14) (2,20) (1,16) (11,12) (11,8) (13,2) (16,4) (11,5) (9,13) (1,0) (0,24) (6,18) (18,21) (3,10) (17,12) (19,11) (16,18) (3,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph351",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,0) (15,9) (0,9) (8,13) (7,8) (6,7) (4,9) (3,15) (12,13) (7,14) (2,15) (11,1) (13,5) (10,14) (0,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph114",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,5) (5,9) (8,7) (9,0) (3,1) (11,0) (8,0) (4,0) (10,11) (6,2) (6,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph827",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,6) (17,1) (2,20) (23,20) (4,10) (0,12) (14,2) (18,23) (19,0) (4,13) (9,17) (16,21) (1,18) (15,8) (11,15) (16,5) (17,3) (6,20) (19,6) (23,7) (16,19) (22,20) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1772",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,1) (21,19) (18,6) (11,12) (3,0) (18,5) (3,12) (7,23) (4,13) (5,4) (11,8) (15,3) (10,2) (18,1) (20,3) (19,11) (12,14) (17,22) (23,21) (20,24) (3,9) (3,17) (11,2) (15,0) (1,0) (0,2) (16,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1183",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,8) (9,12) (9,2) (3,8) (12,10) (5,8) (14,11) (2,0) (4,12) (9,7) (0,6) (1,0) (6,12) (10,13) (14,12) (1,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1269",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,13) (11,7) (2,4) (9,16) (5,11) (3,1) (3,0) (8,2) (16,2) (9,6) (3,14) (2,0) (12,15) (10,11) (0,4) (0,1) (14,7) (13,0) (2,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1128",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,13) (10,13) (0,1) (5,6) (6,2) (0,4) (1,2) (8,9) (3,6) (4,12) (1,11) (7,8) (3,0) (11,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph151",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,10) (4,2) (8,2) (10,9) (7,0) (11,4) (7,6) (1,10) (3,5) (9,12) (11,0) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1717",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (14,13) (7,0) (12,18) (17,0) (6,2) (23,22) (1,13) (21,15) (23,7) (3,9) (5,3) (19,21) (20,4) (10,23) (9,21) (8,11) (1,20) (16,4) (12,17) (0,1) (20,6) (15,12) (6,22) (23,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1752",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (8,24) (24,12) (21,14) (2,21) (12,21) (20,6) (13,23) (16,10) (0,3) (18,2) (1,19) (20,9) (24,5) (14,19) (17,23) (8,3) (1,0) (4,22) (8,15) (23,3) (9,14) (9,16) (22,12) (8,7) (7,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph983",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,0) (4,9) (3,8) (1,0) (5,7) (1,2) (0,2) (2,8) (1,4) (11,5) (7,10) (3,0) (0,6) (4,0) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph492",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (3,15) (15,14) (13,17) (14,2) (10,3) (0,12) (17,8) (10,18) (7,1) (0,11) (18,9) (1,16) (4,6) (13,5) (6,11) (0,1) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph679",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,0) (6,3) (17,10) (9,19) (2,11) (8,18) (12,1) (14,4) (4,8) (21,9) (1,14) (16,7) (3,10) (17,16) (15,1) (20,17) (11,16) (7,19) (1,20) (5,13) (13,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1647",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (21,19) (8,7) (17,20) (3,11) (15,0) (3,21) (17,2) (22,9) (10,11) (0,2) (7,10) (10,13) (1,8) (11,4) (17,15) (16,10) (2,14) (7,22) (5,11) (20,6) (15,12) (4,2) (18,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph637",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,14) (11,17) (18,19) (4,9) (2,17) (8,20) (10,5) (0,16) (8,15) (16,20) (18,3) (6,4) (11,3) (16,1) (9,13) (8,12) (10,7) (10,4) (0,11) (18,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph455",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,6) (8,0) (5,2) (13,2) (3,16) (9,10) (11,4) (1,12) (8,17) (15,12) (10,8) (3,0) (14,7) (0,13) (16,11) (1,13) (12,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph885",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,2) (15,10) (23,14) (22,12) (23,5) (22,9) (16,23) (0,1) (4,8) (4,21) (16,13) (17,14) (16,7) (5,19) (5,1) (11,23) (24,1) (18,0) (11,20) (15,11) (14,6) (1,22) (23,8) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1514",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,11) (16,5) (18,4) (15,14) (16,12) (3,6) (5,1) (16,9) (1,8) (4,8) (2,19) (0,14) (20,7) (17,11) (0,1) (19,5) (6,14) (10,15) (0,3) (11,13) (2,0) (1,11) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1477",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,17) (0,16) (0,1) (19,10) (14,3) (4,14) (18,15) (11,16) (19,8) (4,5) (14,13) (11,6) (9,1) (7,3) (0,12) (18,17) (2,1) (13,19) (11,19) (9,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1160",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (5,3) (10,11) (1,8) (5,11) (13,6) (7,12) (9,4) (4,2) (0,2) (0,9) (6,4) (8,2) (2,12) (5,13) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1535",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (16,9) (1,13) (19,12) (5,7) (2,0) (0,6) (8,12) (5,15) (4,1) (14,10) (3,10) (14,11) (18,8) (0,1) (2,6) (11,20) (4,11) (7,3) (11,8) (17,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1470",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,5) (5,4) (17,2) (19,3) (19,4) (7,4) (15,4) (6,19) (4,1) (6,13) (0,1) (17,6) (14,6) (14,10) (11,13) (5,12) (3,0) (18,6) (9,7) (16,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1694",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,15) (16,15) (8,0) (12,2) (23,22) (4,1) (21,3) (10,13) (6,17) (16,19) (6,5) (9,8) (12,8) (3,7) (11,3) (18,17) (22,19) (11,0) (23,4) (1,0) (10,22) (10,20) (20,14) (17,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1485",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,12) (8,15) (10,2) (1,16) (13,3) (14,8) (15,18) (14,6) (8,2) (19,11) (18,4) (14,0) (16,15) (15,9) (19,8) (11,17) (1,7) (3,10) (13,5) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph693",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (12,0) (5,2) (4,6) (7,9) (11,19) (16,15) (19,0) (10,3) (15,11) (3,14) (2,6) (1,16) (15,7) (10,1) (16,18) (21,4) (1,13) (9,8) (10,20) (17,0) (17,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph508",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,10) (7,16) (4,0) (3,18) (11,12) (0,5) (11,1) (10,8) (6,7) (12,13) (18,12) (11,16) (9,13) (5,16) (0,15) (12,17) (1,2) (14,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph94",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,7) (6,7) (9,11) (1,6) (5,6) (1,2) (4,9) (4,8) (0,1) (7,3) (6,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1570",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,17) (15,10) (2,4) (0,2) (11,4) (11,3) (8,7) (3,0) (15,9) (2,13) (20,3) (0,1) (18,21) (7,21) (14,17) (5,11) (8,1) (11,10) (0,15) (20,6) (10,7) (12,10) (19,17) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1003",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,8) (2,11) (11,0) (1,0) (0,2) (0,7) (3,9) (11,1) (3,2) (0,3) (3,4) (10,5) (4,0) (6,1) (1,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1068",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,5) (8,10) (0,9) (7,2) (8,3) (11,4) (0,2) (7,6) (9,11) (1,3) (1,0) (7,12) (5,11) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph691",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (11,12) (17,3) (5,15) (17,18) (19,20) (12,13) (8,3) (5,4) (9,2) (14,3) (16,1) (19,11) (15,0) (21,3) (2,11) (21,12) (6,18) (10,4) (5,18) (1,19) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1461",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,11) (13,7) (4,0) (11,16) (17,19) (13,15) (3,0) (8,15) (5,17) (2,0) (10,8) (12,7) (10,14) (1,17) (14,0) (1,0) (6,19) (14,17) (1,3) (2,16) (18,3) (4,3) (18,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph540",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,18) (14,19) (10,3) (6,14) (3,2) (18,14) (11,8) (15,7) (10,7) (12,11) (0,6) (19,16) (19,1) (7,5) (17,13) (18,17) (4,6) (18,7) (12,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1774",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,11) (0,14) (1,0) (0,21) (6,5) (0,2) (18,7) (2,22) (12,3) (1,22) (20,23) (15,2) (6,12) (24,19) (10,6) (22,14) (23,14) (21,5) (13,21) (4,22) (24,16) (24,20) (9,23) (5,8) (9,18) (17,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph127",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,8) (7,10) (7,3) (4,8) (0,2) (7,4) (9,12) (9,5) (6,3) (6,11) (7,1) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1547",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,9) (0,3) (0,4) (17,8) (16,0) (19,8) (11,17) (0,10) (12,20) (20,18) (7,5) (1,4) (2,18) (10,3) (2,17) (8,7) (0,2) (15,20) (16,13) (2,9) (0,1) (11,13) (14,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1207",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,14) (3,12) (11,13) (15,11) (2,0) (9,14) (5,2) (5,14) (5,1) (1,0) (15,6) (8,12) (8,7) (6,14) (10,14) (6,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph967",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,0) (3,0) (3,6) (2,8) (0,9) (10,7) (10,8) (1,2) (7,4) (4,3) (8,9) (5,10) (11,2) (0,4) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph709",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,19) (12,15) (16,12) (11,15) (20,17) (9,21) (0,2) (13,10) (2,6) (7,5) (10,12) (4,3) (9,5) (8,2) (12,18) (9,4) (2,11) (1,6) (17,13) (21,20) (14,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1042",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,4) (4,1) (4,0) (11,12) (11,8) (1,0) (10,8) (3,0) (3,8) (9,5) (2,11) (3,6) (0,2) (1,7) (5,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph963",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (5,0) (4,0) (11,7) (3,2) (5,10) (4,10) (8,2) (2,0) (10,7) (1,0) (6,7) (0,3) (1,9) (11,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1052",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,10) (7,3) (0,2) (0,8) (10,12) (3,0) (0,1) (1,11) (3,6) (9,6) (3,4) (9,8) (12,11) (12,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph559",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,12) (2,11) (3,1) (7,14) (19,10) (13,12) (2,5) (2,9) (16,11) (15,9) (1,0) (6,11) (17,16) (14,3) (0,13) (2,19) (17,4) (19,8) (7,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph425",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,14) (8,0) (9,4) (12,15) (17,14) (6,0) (3,2) (10,16) (9,5) (5,10) (13,12) (7,1) (7,4) (15,9) (0,11) (5,17) (0,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1016",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (0,2) (8,11) (9,2) (0,10) (2,4) (5,6) (2,10) (7,1) (0,5) (8,5) (1,0) (9,3) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1112",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,3) (0,11) (13,7) (5,9) (12,5) (2,8) (12,3) (1,0) (7,1) (4,5) (7,0) (11,12) (0,3) (0,2) (2,6) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1255",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,1) (2,14) (9,12) (0,2) (4,2) (4,13) (5,7) (0,12) (15,10) (7,11) (0,1) (1,9) (0,3) (9,6) (3,12) (15,11) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1061",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (0,1) (0,2) (12,2) (8,10) (3,4) (7,0) (10,12) (4,11) (1,6) (5,0) (9,7) (0,12) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1033",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,0) (1,5) (7,2) (3,4) (8,6) (7,9) (4,11) (0,1) (10,1) (0,3) (9,6) (8,10) (11,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph547",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (4,1) (19,6) (5,16) (1,10) (12,7) (11,8) (9,6) (16,4) (18,14) (2,14) (14,8) (19,14) (11,15) (3,18) (4,13) (7,9) (1,6) (16,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1475",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,15) (14,4) (1,15) (0,2) (9,12) (18,4) (16,7) (0,3) (15,19) (4,6) (19,14) (8,14) (0,1) (13,8) (7,17) (5,11) (19,0) (2,8) (0,10) (16,3) (11,12) (0,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1334",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,15) (1,0) (15,2) (8,5) (1,7) (3,0) (14,6) (11,10) (13,17) (6,13) (0,10) (0,5) (15,8) (0,4) (8,0) (11,12) (4,9) (17,15) (0,2) (16,17) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph795",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,20) (13,8) (10,5) (18,22) (13,9) (6,4) (23,1) (16,0) (22,21) (9,4) (11,3) (20,11) (16,17) (16,23) (17,2) (18,3) (10,12) (8,19) (15,1) (7,23) (18,14) (10,4) (0,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1657",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,14) (0,1) (2,5) (11,13) (13,0) (3,8) (9,13) (11,15) (19,8) (17,1) (3,0) (21,10) (20,13) (12,15) (17,0) (13,6) (5,9) (7,0) (3,4) (0,2) (9,16) (21,0) (22,14) (8,17) (19,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1728",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,16) (1,19) (3,12) (7,12) (17,12) (12,14) (15,11) (16,5) (1,0) (11,0) (6,22) (17,13) (18,0) (2,8) (12,1) (11,9) (10,11) (7,5) (2,0) (21,7) (22,19) (17,4) (0,3) (8,13) (17,20) (0,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph254",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,7) (9,2) (2,0) (3,11) (3,10) (14,5) (2,1) (6,5) (12,3) (1,5) (7,2) (4,7) (8,9) (11,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph541",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (12,11) (13,16) (3,2) (7,10) (7,19) (1,8) (18,17) (2,14) (5,15) (4,14) (12,5) (3,16) (6,10) (1,6) (0,4) (9,14) (8,14) (11,13) (17,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph781",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,5) (21,20) (15,0) (10,1) (14,22) (6,12) (4,15) (1,4) (9,21) (8,4) (1,21) (17,3) (17,7) (12,3) (2,0) (19,1) (22,23) (17,23) (4,11) (23,18) (7,13) (16,4) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1397",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,14) (2,9) (0,14) (2,15) (2,17) (7,4) (4,10) (9,6) (1,0) (10,18) (12,2) (13,2) (16,6) (7,1) (14,12) (11,8) (9,5) (15,8) (9,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1304",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,1) (3,12) (0,2) (8,5) (10,9) (16,7) (0,5) (7,4) (3,8) (0,1) (14,9) (4,0) (8,7) (12,14) (11,2) (6,8) (9,13) (2,14) (3,0) (15,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1089",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,0) (5,4) (10,1) (11,1) (1,12) (10,13) (1,8) (10,7) (4,3) (1,0) (7,2) (4,7) (6,9) (6,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph72",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,7) (11,9) (2,3) (7,10) (11,7) (2,0) (5,9) (5,4) (3,11) (2,6) (8,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1266",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,13) (2,3) (12,6) (1,16) (16,5) (8,3) (6,7) (12,11) (0,2) (14,9) (8,4) (9,4) (1,0) (15,3) (10,16) (16,11) (13,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1693",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (19,7) (10,18) (17,21) (21,20) (11,10) (0,1) (15,13) (0,2) (22,3) (16,17) (6,23) (20,8) (11,5) (22,12) (3,0) (14,10) (15,2) (10,7) (6,7) (0,15) (4,0) (2,4) (9,7) (8,1) (11,4) (17,2) (3,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph673",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,17) (11,6) (11,1) (8,0) (16,19) (12,9) (4,0) (6,18) (0,18) (20,15) (2,16) (5,17) (14,0) (10,2) (13,3) (14,13) (20,6) (16,3) (21,1) (12,3) (10,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1081",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,1) (6,5) (9,7) (12,3) (0,3) (13,4) (1,13) (0,2) (10,4) (12,11) (8,12) (4,7) (8,1) (4,2) (3,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph274",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,0) (3,12) (6,13) (10,9) (11,9) (3,4) (9,7) (6,0) (2,12) (8,1) (13,10) (4,0) (6,14) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph382",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,16) (16,6) (4,15) (9,6) (9,2) (1,4) (10,13) (13,7) (5,11) (3,12) (0,10) (4,5) (16,8) (6,7) (3,15) (16,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1078",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,6) (2,10) (10,5) (3,12) (8,10) (10,4) (2,3) (4,1) (4,0) (2,7) (10,11) (3,9) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1342",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,4) (0,12) (9,10) (13,2) (13,9) (6,0) (0,7) (5,11) (17,8) (11,12) (15,16) (0,1) (3,4) (16,1) (2,11) (3,10) (14,7) (8,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph190",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,0) (7,0) (4,9) (6,5) (5,8) (1,11) (8,1) (6,3) (9,13) (12,3) (8,10) (10,2) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph452",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,15) (12,15) (11,0) (4,7) (17,5) (7,1) (0,6) (2,3) (9,5) (10,16) (14,2) (9,4) (0,8) (13,12) (15,0) (10,5) (14,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph249",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,9) (8,0) (13,8) (0,10) (10,6) (3,9) (1,4) (9,5) (12,10) (2,10) (7,13) (14,10) (1,14) (13,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1598",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (13,20) (20,6) (9,21) (1,10) (8,14) (0,2) (14,0) (0,16) (18,3) (11,8) (17,6) (9,7) (21,6) (11,19) (0,3) (21,15) (5,16) (7,12) (2,14) (4,18) (16,4) (1,20) (1,4) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph353",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (2,4) (12,2) (6,3) (11,8) (5,7) (15,2) (6,13) (1,12) (15,13) (14,6) (7,4) (10,7) (9,5) (12,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph777",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (21,13) (13,15) (0,7) (0,9) (20,9) (10,21) (4,21) (6,13) (3,15) (18,20) (1,11) (5,9) (14,12) (15,2) (19,7) (14,0) (16,22) (7,11) (22,4) (9,10) (8,7) (8,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph599",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,2) (7,0) (4,19) (16,10) (4,12) (14,11) (9,5) (11,9) (5,17) (1,16) (6,9) (10,12) (12,7) (13,8) (16,8) (15,8) (13,18) (0,3) (17,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1611",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,15) (1,8) (8,20) (15,21) (17,20) (0,3) (19,16) (2,10) (0,1) (8,0) (9,15) (17,4) (7,10) (12,17) (21,18) (3,6) (7,14) (3,9) (6,11) (13,19) (16,0) (6,5) (2,0) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1552",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,7) (4,2) (18,2) (0,12) (5,8) (3,0) (1,9) (20,5) (13,3) (4,15) (3,12) (12,17) (1,7) (8,11) (17,11) (9,10) (16,7) (16,17) (9,19) (0,1) (0,2) (14,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph780",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,11) (15,9) (16,13) (12,20) (2,10) (3,7) (18,8) (18,6) (23,6) (0,22) (18,0) (21,6) (1,17) (10,20) (5,15) (16,14) (8,20) (7,17) (13,22) (9,17) (4,0) (2,19) (19,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph740",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,7) (11,3) (16,9) (9,7) (7,10) (7,13) (1,0) (9,6) (10,2) (0,22) (9,18) (8,6) (2,20) (14,19) (21,9) (14,15) (12,5) (17,10) (13,12) (1,11) (4,14) (17,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph950",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,0) (7,4) (5,3) (10,9) (10,1) (3,7) (7,10) (0,1) (2,1) (3,8) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1158",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (7,10) (10,14) (1,0) (0,2) (1,2) (2,10) (4,7) (14,11) (0,4) (12,8) (3,13) (9,4) (5,3) (0,3) (13,14) (8,14) (6,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1157",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,7) (2,0) (4,1) (13,12) (11,3) (3,9) (14,3) (0,12) (10,3) (4,2) (6,5) (1,13) (7,4) (3,5) (9,8) (0,3) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph801",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,6) (6,5) (19,13) (18,2) (17,1) (8,14) (3,18) (6,23) (0,3) (1,6) (12,21) (18,9) (4,6) (13,9) (8,22) (20,14) (12,11) (14,19) (7,23) (11,9) (16,6) (15,0) (10,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph800",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,20) (18,11) (13,3) (15,6) (21,0) (9,14) (1,5) (10,13) (13,2) (5,19) (9,15) (11,0) (22,0) (2,4) (8,22) (7,23) (18,13) (12,20) (16,15) (17,6) (5,16) (7,4) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1192",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,4) (0,8) (6,1) (14,4) (10,8) (0,1) (8,11) (11,12) (5,7) (4,6) (12,3) (2,12) (11,13) (0,3) (10,4) (9,2) (2,0) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph578",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,6) (10,1) (8,16) (17,15) (0,13) (12,4) (18,2) (7,8) (5,4) (14,15) (11,4) (14,10) (12,1) (9,18) (3,9) (0,7) (13,19) (1,7) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph810",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (14,17) (5,14) (2,16) (11,3) (11,6) (22,0) (8,16) (1,19) (10,5) (4,3) (0,19) (5,9) (18,16) (13,9) (8,20) (22,23) (3,12) (14,21) (6,15) (10,8) (10,7) (14,3) (19,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph715",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,10) (19,14) (11,15) (6,9) (0,7) (2,11) (2,1) (4,13) (3,19) (10,13) (2,18) (14,5) (6,17) (5,18) (19,0) (12,8) (2,10) (8,4) (9,21) (21,7) (16,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1306",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,1) (8,11) (6,9) (0,3) (7,10) (6,16) (4,12) (14,0) (9,7) (11,13) (0,1) (16,3) (0,2) (14,8) (2,14) (4,1) (4,15) (16,0) (6,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph318",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,11) (3,0) (6,8) (2,5) (3,15) (12,11) (12,0) (12,7) (12,8) (10,13) (7,5) (7,4) (14,8) (7,1) (9,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1697",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,0) (17,21) (23,6) (14,18) (11,19) (3,18) (12,4) (20,13) (15,6) (1,0) (2,15) (21,4) (17,22) (23,21) (5,2) (23,18) (0,10) (8,7) (10,11) (8,0) (0,4) (15,8) (1,9) (15,16) (0,3) (2,0) (13,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1267",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,6) (7,3) (12,8) (16,15) (2,0) (12,0) (14,15) (11,1) (14,0) (6,13) (7,16) (7,4) (9,4) (4,2) (2,1) (0,1) (6,12) (5,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph435",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,4) (6,9) (16,7) (0,12) (1,7) (12,17) (7,5) (2,0) (8,3) (2,13) (17,16) (9,14) (4,11) (9,1) (15,10) (12,3) (15,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph756",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,16) (0,17) (7,5) (10,11) (12,7) (6,22) (4,17) (13,8) (12,17) (13,17) (11,15) (16,18) (18,22) (12,3) (1,19) (9,11) (21,19) (2,8) (12,14) (0,11) (7,20) (12,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph873",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,17) (11,9) (22,7) (2,8) (6,22) (16,5) (15,11) (10,11) (17,13) (11,0) (8,13) (14,12) (1,19) (5,7) (0,24) (12,1) (17,20) (7,12) (23,19) (18,16) (17,24) (21,12) (12,3) (0,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1619",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (13,20) (7,19) (12,9) (11,21) (14,6) (13,14) (4,19) (18,20) (16,8) (6,17) (5,3) (0,5) (15,1) (0,4) (6,0) (1,0) (0,12) (10,17) (3,0) (21,2) (2,0) (20,8) (2,4) (20,3) (6,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1094",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,12) (3,1) (5,9) (2,5) (10,0) (0,1) (11,0) (13,1) (0,2) (10,7) (6,8) (11,12) (3,6) (0,13) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph434",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,13) (12,4) (7,2) (0,11) (6,9) (3,14) (1,13) (12,9) (10,2) (6,5) (17,9) (10,9) (14,16) (15,14) (7,15) (11,7) (1,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph887",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,5) (0,20) (9,8) (1,15) (11,15) (16,0) (19,11) (2,22) (2,24) (17,4) (10,14) (10,6) (10,9) (10,5) (21,12) (22,16) (7,6) (14,12) (10,20) (18,15) (11,2) (13,22) (0,17) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph573",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,15) (1,8) (15,7) (7,5) (16,10) (17,14) (9,2) (2,6) (12,11) (13,8) (4,6) (8,11) (17,7) (9,3) (12,5) (8,10) (0,15) (19,18) (2,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph778",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,22) (16,10) (12,6) (4,17) (2,17) (9,5) (18,10) (14,19) (9,15) (18,12) (6,1) (2,19) (4,0) (12,11) (1,15) (17,15) (7,14) (6,20) (7,13) (21,14) (3,14) (15,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph65",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,11) (7,10) (9,2) (2,0) (5,4) (4,1) (7,1) (1,3) (6,10) (8,7) (7,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph951",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,0) (1,0) (3,0) (5,6) (9,6) (2,1) (7,10) (2,0) (8,4) (4,0) (9,4) (6,1) (7,3) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph108",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,10) (8,0) (3,8) (8,2) (8,4) (4,9) (2,5) (7,8) (1,5) (11,6) (3,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1294",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,13) (1,5) (10,14) (6,14) (16,6) (15,11) (3,12) (14,5) (15,6) (8,12) (7,8) (2,5) (3,0) (2,0) (1,0) (9,14) (4,14) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph879",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,21) (14,8) (4,21) (13,21) (3,15) (24,10) (10,14) (4,3) (23,7) (20,12) (2,16) (5,22) (21,22) (13,12) (19,6) (6,22) (3,0) (9,14) (19,18) (11,4) (16,10) (7,12) (1,9) (2,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph41",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (3,9) (4,10) (9,7) (8,4) (6,0) (8,6) (1,9) (8,2) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1218",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,0) (6,10) (6,3) (1,8) (9,1) (15,10) (9,13) (1,11) (1,0) (12,2) (0,4) (5,9) (7,15) (13,3) (14,3) (12,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1480",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,0) (1,10) (13,0) (7,1) (4,5) (9,18) (2,5) (15,17) (1,0) (0,2) (9,6) (12,1) (18,2) (14,10) (16,8) (14,15) (13,19) (12,4) (4,11) (3,9) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1599",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (12,17) (6,14) (18,2) (18,9) (6,5) (6,4) (20,8) (12,11) (1,0) (11,9) (9,13) (8,14) (0,15) (6,10) (7,20) (18,3) (15,21) (1,6) (14,19) (1,16) (3,0) (19,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph665",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,17) (9,4) (6,8) (19,0) (17,16) (20,19) (10,15) (7,17) (13,2) (1,18) (16,19) (14,8) (12,4) (1,15) (2,20) (6,18) (16,5) (0,11) (6,20) (0,4) (20,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1001",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,9) (0,7) (10,0) (0,2) (1,0) (11,4) (3,8) (2,4) (1,5) (0,4) (6,2) (0,11) (0,3) (7,3) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph85",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,2) (4,7) (7,1) (3,9) (0,6) (0,10) (5,7) (10,3) (0,8) (2,6) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1787",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,21) (21,13) (23,14) (4,0) (1,20) (14,4) (20,17) (6,3) (18,24) (5,13) (8,22) (2,0) (24,9) (3,0) (11,16) (24,19) (1,0) (1,12) (15,1) (16,17) (2,11) (8,4) (3,10) (1,23) (17,10) (7,19) (7,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph200",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,5) (8,12) (5,0) (8,6) (5,6) (5,10) (2,6) (7,13) (0,13) (11,4) (1,4) (8,3) (9,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1483",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,18) (13,1) (11,10) (15,9) (13,4) (14,5) (0,2) (10,19) (18,9) (10,8) (14,7) (2,3) (13,0) (1,19) (11,12) (16,11) (0,1) (8,17) (6,3) (15,19) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph611",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,0) (6,2) (4,5) (7,2) (0,3) (20,8) (5,18) (13,5) (16,12) (9,10) (8,17) (0,15) (18,1) (5,11) (14,5) (3,5) (20,15) (7,14) (19,15) (11,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1707",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (15,3) (1,4) (6,18) (18,4) (13,19) (17,12) (2,8) (0,19) (15,0) (23,8) (8,14) (23,22) (11,15) (10,14) (5,2) (7,3) (0,22) (9,15) (12,13) (20,16) (6,3) (21,14) (20,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph696",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,17) (12,5) (21,18) (8,10) (6,2) (15,2) (2,20) (20,0) (8,14) (15,7) (5,7) (16,17) (8,11) (3,8) (1,15) (12,11) (18,20) (9,6) (13,2) (9,4) (7,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph700",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,0) (9,5) (15,9) (21,10) (19,16) (14,11) (13,0) (6,13) (17,8) (17,1) (9,13) (5,2) (3,8) (13,19) (21,11) (0,20) (18,8) (4,3) (17,0) (11,13) (15,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph194",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,4) (3,10) (13,8) (1,2) (6,2) (7,1) (5,13) (10,0) (12,3) (0,6) (13,3) (9,7) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1374",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,0) (17,15) (3,12) (1,0) (1,7) (0,5) (1,9) (4,0) (17,12) (8,3) (14,9) (12,0) (7,16) (13,2) (11,4) (15,10) (7,5) (17,16) (6,9) (0,3) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1283",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,0) (16,12) (2,11) (8,14) (1,0) (5,2) (3,1) (6,10) (0,2) (10,15) (9,13) (16,13) (4,14) (14,11) (3,5) (13,7) (14,10) (13,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph449",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,0) (12,17) (9,6) (9,2) (4,11) (14,17) (17,4) (11,13) (16,8) (0,5) (14,16) (14,6) (1,15) (1,3) (10,15) (10,7) (8,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph797",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,2) (12,1) (0,18) (12,7) (0,11) (10,11) (4,17) (12,14) (17,20) (7,5) (17,12) (11,9) (22,6) (23,0) (1,19) (18,16) (15,11) (13,17) (22,19) (12,3) (8,13) (21,7) (5,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph461",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,2) (6,7) (5,6) (17,0) (13,14) (3,13) (3,0) (15,17) (14,8) (10,4) (12,17) (1,6) (7,10) (9,11) (11,12) (7,16) (14,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph870",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (14,24) (2,6) (13,24) (6,8) (1,23) (17,15) (16,5) (4,24) (17,10) (13,6) (20,13) (7,23) (16,19) (15,1) (21,19) (23,13) (22,7) (0,23) (3,21) (9,19) (11,1) (20,5) (12,4) (18,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph650",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (5,17) (7,4) (5,14) (13,1) (1,20) (18,10) (15,3) (19,5) (19,0) (17,13) (1,8) (3,20) (4,6) (14,12) (9,0) (7,2) (11,16) (19,10) (2,11) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1240",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,10) (2,0) (13,0) (2,11) (2,15) (9,6) (2,8) (12,13) (4,2) (3,1) (11,9) (7,14) (11,5) (1,0) (14,3) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1762",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,9) (9,13) (0,2) (10,17) (20,0) (21,7) (3,0) (11,8) (23,2) (4,8) (1,0) (22,20) (23,18) (19,17) (2,6) (1,15) (11,12) (8,10) (7,5) (20,24) (8,16) (22,3) (2,15) (14,2) (7,15) (12,5) (20,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph465",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,12) (1,9) (11,4) (0,2) (13,9) (6,8) (7,16) (4,6) (2,3) (8,14) (5,9) (13,11) (0,14) (15,0) (7,14) (0,17) (10,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1400",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,6) (1,6) (2,14) (3,0) (1,0) (4,13) (3,18) (10,1) (11,8) (16,4) (9,6) (11,15) (7,12) (14,18) (0,16) (5,16) (8,14) (9,7) (4,1) (0,2) (17,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1095",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,6) (0,5) (6,8) (11,5) (1,0) (8,4) (9,7) (6,9) (8,3) (0,2) (6,1) (3,0) (5,4) (10,7) (0,4) (2,1) (13,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1495",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,16) (12,14) (17,15) (18,10) (0,8) (1,0) (13,0) (0,15) (7,1) (4,7) (0,2) (19,5) (0,6) (11,19) (15,12) (4,9) (5,9) (2,14) (10,5) (2,3) (17,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1491",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,16) (5,15) (1,0) (5,18) (4,17) (2,0) (3,6) (16,7) (13,14) (16,10) (19,2) (15,9) (6,14) (1,11) (5,1) (11,12) (14,0) (8,1) (19,11) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph927",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,6) (0,9) (1,4) (7,3) (6,1) (8,2) (10,2) (3,10) (1,0) (0,5) (9,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph642",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,12) (6,17) (0,13) (2,13) (18,9) (3,0) (1,18) (11,4) (15,8) (5,2) (14,7) (13,1) (11,10) (8,0) (14,16) (12,19) (3,19) (15,20) (17,12) (8,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1021",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,2) (10,2) (4,7) (10,12) (5,10) (7,10) (3,4) (9,8) (2,1) (11,8) (3,6) (0,9) (3,0) (0,2) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1740",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (22,13) (3,21) (1,0) (24,6) (21,4) (3,0) (16,23) (1,10) (24,17) (12,9) (13,5) (10,22) (7,20) (15,20) (5,4) (9,16) (15,3) (0,2) (18,22) (11,17) (6,7) (6,14) (8,17) (16,17) (4,2) (0,4) (19,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph204",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,13) (3,6) (4,0) (11,8) (1,11) (1,2) (12,4) (6,5) (3,0) (2,6) (8,9) (13,10) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph895",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,15) (11,10) (21,24) (3,1) (17,20) (13,15) (10,16) (18,15) (19,5) (6,20) (9,14) (0,5) (14,8) (8,22) (7,6) (12,7) (9,15) (2,21) (23,24) (10,3) (16,21) (8,6) (4,14) (3,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1239",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,9) (9,15) (9,2) (15,14) (5,10) (3,8) (1,7) (15,4) (11,2) (6,5) (13,12) (7,15) (9,13) (8,14) (5,0) (0,1) (3,0) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1141",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,0) (12,2) (13,4) (4,10) (13,12) (5,14) (7,10) (6,13) (6,1) (13,8) (0,14) (3,14) (0,9) (2,0) (1,0) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph632",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (5,14) (0,10) (14,15) (16,13) (19,6) (8,4) (14,3) (16,19) (4,5) (10,2) (12,5) (1,19) (14,20) (10,17) (12,1) (18,2) (7,11) (0,11) (19,17) (8,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph562",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,17) (11,12) (0,14) (19,8) (10,2) (15,9) (19,11) (7,1) (18,4) (8,14) (3,10) (5,13) (16,1) (6,14) (8,15) (18,15) (8,2) (13,3) (16,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1630",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,15) (8,21) (13,6) (14,16) (9,2) (15,17) (18,15) (0,5) (10,22) (16,0) (12,10) (22,17) (19,11) (3,1) (8,16) (21,7) (4,17) (19,4) (1,0) (10,9) (14,6) (14,12) (0,2) (11,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph211",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,1) (1,11) (2,11) (13,12) (10,5) (9,0) (0,3) (2,7) (2,4) (10,11) (5,12) (6,3) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph793",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (11,8) (23,6) (4,9) (5,0) (3,4) (14,18) (6,13) (21,7) (15,10) (1,23) (18,15) (18,19) (17,10) (16,3) (5,20) (10,4) (3,2) (20,12) (2,22) (8,21) (14,13) (0,13) (21,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1532",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,9) (1,0) (9,6) (13,1) (7,15) (14,15) (12,4) (2,0) (10,7) (5,6) (3,14) (1,8) (17,10) (9,7) (9,19) (14,16) (2,10) (9,13) (20,17) (11,0) (7,11) (18,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1782",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,0) (8,17) (6,13) (5,13) (13,23) (23,3) (17,3) (14,7) (2,0) (2,22) (5,15) (8,9) (14,19) (16,14) (23,24) (21,11) (9,1) (11,23) (22,4) (15,18) (16,4) (7,10) (20,2) (9,12) (5,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1056",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,7) (5,12) (1,0) (7,8) (2,4) (7,3) (1,4) (10,8) (6,3) (9,7) (0,6) (8,5) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1105",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,2) (0,2) (7,10) (6,4) (3,4) (2,9) (0,1) (11,7) (5,0) (8,9) (0,12) (3,12) (7,5) (12,13) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph336",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,13) (2,1) (11,6) (13,12) (10,0) (2,8) (3,11) (10,1) (2,15) (5,4) (1,7) (1,6) (3,9) (4,12) (14,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph32",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,6) (10,1) (10,7) (7,0) (4,7) (4,3) (2,7) (5,4) (6,1) (1,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1674",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,21) (14,15) (20,7) (7,8) (1,12) (0,1) (13,0) (21,2) (5,13) (9,18) (20,0) (0,2) (18,2) (4,11) (4,12) (5,19) (17,15) (10,14) (3,0) (3,9) (1,10) (8,16) (6,9) (7,1) (5,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph22",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,8) (0,6) (8,5) (3,9) (1,10) (10,4) (9,1) (4,8) (8,2) (9,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1030",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,3) (0,2) (2,12) (8,12) (7,0) (8,11) (8,7) (0,1) (10,9) (6,7) (7,5) (1,8) (2,3) (4,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph240",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,2) (14,6) (0,8) (1,5) (7,11) (8,13) (8,2) (3,11) (11,12) (4,10) (3,8) (12,4) (9,8) (6,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph760",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (20,13) (1,19) (11,17) (5,7) (15,6) (8,19) (2,3) (21,10) (18,21) (20,12) (6,19) (9,14) (22,17) (5,21) (16,12) (18,1) (0,1) (13,5) (2,11) (16,11) (2,4) (9,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph677",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,18) (12,11) (5,14) (18,8) (20,8) (15,20) (5,11) (13,16) (2,6) (9,21) (17,0) (9,10) (5,16) (0,15) (7,14) (21,15) (7,2) (5,3) (5,4) (5,19) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph349",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,11) (6,14) (12,1) (4,1) (13,9) (11,1) (15,2) (11,5) (6,12) (1,8) (10,15) (9,2) (13,7) (0,11) (15,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph208",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,10) (7,13) (8,5) (3,7) (1,4) (11,10) (2,12) (7,10) (6,7) (7,2) (5,3) (9,3) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1353",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,11) (8,6) (14,7) (0,15) (1,9) (3,2) (0,1) (0,3) (8,14) (16,12) (12,10) (0,2) (13,9) (9,5) (0,14) (17,0) (6,4) (7,16) (4,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph95",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,3) (5,7) (6,0) (1,2) (9,3) (1,7) (0,8) (4,7) (10,0) (6,2) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1363",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,14) (12,9) (0,1) (2,10) (12,4) (9,6) (13,1) (0,11) (14,3) (7,15) (11,7) (13,9) (17,9) (8,1) (7,2) (5,6) (9,10) (16,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1675",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,10) (2,0) (11,5) (1,13) (0,1) (4,7) (20,15) (4,9) (2,4) (17,20) (12,15) (14,12) (15,18) (7,3) (7,16) (12,8) (14,21) (18,22) (6,16) (12,6) (22,11) (0,19) (2,1) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1639",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,2) (6,15) (5,13) (21,10) (19,8) (11,2) (2,4) (5,21) (21,18) (18,1) (20,13) (12,20) (4,0) (16,12) (17,22) (1,0) (0,2) (11,17) (6,19) (3,0) (0,5) (1,19) (11,16) (9,8) (14,9) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,8) (8,4) (5,10) (3,10) (4,9) (0,7) (0,2) (3,6) (7,8) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph785",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (19,12) (19,15) (4,2) (14,5) (7,23) (22,18) (10,11) (8,14) (23,3) (22,15) (5,13) (22,9) (3,6) (2,11) (21,15) (9,5) (17,7) (11,0) (23,13) (4,20) (16,7) (4,1) (6,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph29",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,1) (10,3) (0,9) (2,3) (5,6) (6,2) (3,4) (0,1) (5,7) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph757",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,20) (8,12) (19,22) (4,10) (0,22) (10,7) (16,1) (9,4) (11,17) (18,3) (0,16) (8,15) (18,20) (2,17) (10,5) (1,14) (6,4) (13,18) (13,9) (11,0) (21,16) (3,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph164",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,8) (11,4) (2,4) (1,7) (12,1) (3,2) (9,0) (9,1) (5,3) (5,1) (12,10) (8,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph453",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,6) (9,8) (15,11) (16,12) (11,17) (2,3) (1,5) (2,11) (16,14) (6,1) (10,9) (13,5) (12,13) (14,17) (5,7) (0,1) (2,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1592",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,17) (3,0) (9,5) (7,0) (11,13) (2,0) (13,19) (5,2) (13,9) (6,13) (13,0) (20,0) (15,9) (10,21) (21,11) (12,15) (17,1) (3,8) (0,17) (16,19) (11,14) (3,4) (18,8) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1373",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,11) (9,12) (5,13) (0,1) (2,8) (2,15) (10,16) (3,10) (12,6) (10,11) (3,6) (8,17) (14,1) (10,7) (5,0) (13,10) (0,2) (0,3) (8,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph64",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,6) (2,0) (7,8) (2,11) (10,6) (10,3) (11,8) (7,4) (3,7) (5,6) (4,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1725",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,9) (22,12) (3,12) (16,5) (13,9) (19,11) (18,4) (2,0) (18,12) (10,15) (20,13) (1,0) (7,14) (2,1) (6,19) (0,8) (11,12) (20,0) (19,16) (21,5) (1,11) (3,23) (16,7) (0,23) (17,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-medium-graph253",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,3) (10,3) (7,2) (14,4) (10,0) (1,11) (8,5) (12,13) (4,9) (11,6) (4,7) (13,8) (1,4) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-medium-graph1493",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,4) (5,15) (9,17) (1,18) (16,14) (3,0) (1,0) (1,10) (18,3) (0,4) (12,18) (16,15) (0,2) (7,18) (8,3) (10,17) (2,5) (13,8) (2,18) (16,6) (19,0) (11,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph13",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,16) (9,7) (25,19) (6,0) (23,6) (23,21) (1,9) (15,11) (19,24) (0,5) (1,8) (6,16) (22,3) (24,14) (8,15) (13,17) (18,9) (18,20) (4,24) (2,12) (21,18) (12,1) (20,10) (13,3) (3,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1374",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,9) (13,10) (6,16) (25,19) (23,15) (12,2) (5,24) (4,24) (25,8) (9,22) (8,28) (11,15) (12,25) (8,1) (24,3) (1,0) (26,6) (18,11) (16,4) (19,3) (18,28) (27,0) (7,28) (13,1) (21,26) (16,14) (2,0) (12,20) (15,17) (9,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph726",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,7) (29,27) (0,20) (23,0) (2,13) (4,29) (4,18) (12,8) (0,32) (1,11) (0,12) (17,4) (5,24) (1,18) (6,25) (22,27) (3,16) (19,31) (24,6) (22,14) (21,23) (19,17) (26,27) (25,10) (22,28) (27,16) (9,14) (16,13) (25,32) (20,16) (15,11) (30,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1229",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,0) (9,19) (26,19) (5,26) (6,8) (18,26) (2,0) (17,20) (2,4) (16,7) (0,1) (19,27) (2,5) (23,14) (12,1) (12,22) (25,26) (17,3) (6,21) (0,13) (19,15) (9,11) (10,25) (16,24) (4,20) (20,12) (1,8) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1548",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (20,1) (26,24) (15,25) (10,24) (17,16) (18,9) (4,14) (9,19) (21,25) (19,28) (10,3) (2,11) (3,0) (7,16) (14,23) (20,17) (0,1) (11,3) (5,13) (16,13) (8,29) (23,24) (27,28) (7,27) (17,12) (23,1) (22,1) (18,30) (21,1) (6,29) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1903",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,6) (34,22) (32,5) (31,18) (8,14) (20,19) (1,15) (2,0) (21,10) (6,7) (29,9) (0,3) (0,1) (19,16) (17,24) (23,2) (16,33) (1,13) (28,23) (25,10) (19,5) (5,6) (4,5) (30,5) (27,7) (12,5) (33,11) (24,19) (8,19) (21,34) (20,29) (31,0) (26,11) (2,12) (14,3) (31,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1583",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,0) (23,30) (29,16) (30,27) (20,12) (12,7) (17,4) (21,11) (30,16) (26,7) (17,24) (22,8) (12,3) (19,28) (30,10) (19,1) (30,5) (26,22) (1,0) (9,27) (13,14) (12,1) (7,5) (13,11) (15,11) (17,18) (25,29) (0,11) (2,0) (24,12) (2,8) (28,6) (17,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1766",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,2) (2,0) (29,26) (17,28) (7,29) (17,9) (30,4) (9,23) (1,3) (14,27) (25,30) (5,20) (0,4) (22,30) (24,23) (28,31) (5,0) (14,11) (1,2) (0,1) (4,15) (13,2) (4,29) (20,16) (7,27) (18,8) (8,1) (21,32) (21,18) (0,3) (19,3) (6,25) (14,21) (5,25) (9,12) (9,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph996",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,28) (11,27) (30,19) (19,24) (17,31) (16,13) (3,10) (21,11) (27,32) (12,23) (5,29) (12,15) (28,34) (2,34) (13,23) (25,4) (16,2) (26,5) (20,13) (25,24) (23,24) (6,29) (13,18) (31,22) (22,24) (8,29) (16,10) (9,29) (24,11) (7,28) (33,21) (0,5) (11,1) (15,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph703",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (17,24) (1,14) (25,28) (10,7) (11,21) (32,3) (30,19) (16,32) (9,11) (8,0) (20,23) (2,12) (6,7) (11,27) (5,17) (9,26) (6,12) (31,13) (32,19) (23,6) (17,22) (11,25) (1,8) (23,30) (18,2) (21,29) (15,12) (5,0) (31,10) (8,4) (23,24) (16,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1016",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,6) (25,20) (10,12) (1,12) (2,0) (25,15) (11,4) (1,0) (6,18) (2,7) (1,2) (9,5) (0,15) (22,2) (24,20) (13,1) (9,11) (15,6) (17,25) (8,4) (17,9) (4,13) (1,14) (6,23) (3,0) (0,4) (5,21) (3,14) (20,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1980",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,3) (25,17) (7,11) (1,32) (25,23) (9,29) (34,26) (21,17) (18,23) (15,8) (3,25) (24,27) (4,34) (32,12) (1,15) (2,29) (28,9) (32,30) (7,20) (2,0) (20,22) (0,1) (13,4) (3,16) (6,27) (8,6) (5,22) (14,31) (26,10) (20,24) (0,4) (14,18) (2,19) (22,17) (33,13) (2,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1609",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,13) (1,0) (8,22) (22,23) (3,13) (18,7) (7,20) (12,22) (31,10) (9,12) (13,25) (17,29) (14,19) (9,11) (17,24) (6,25) (27,16) (28,21) (16,3) (30,11) (4,11) (27,15) (14,21) (29,2) (1,29) (26,23) (10,24) (29,25) (5,7) (0,9) (13,26) (29,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1080",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,22) (11,2) (24,11) (11,16) (8,19) (10,15) (6,11) (19,10) (17,25) (7,25) (0,1) (19,18) (1,3) (13,0) (9,2) (17,4) (7,20) (14,20) (13,12) (0,3) (21,9) (2,0) (2,15) (17,19) (12,23) (2,5) (3,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph213",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,27) (13,18) (6,17) (16,19) (3,20) (1,13) (0,19) (22,17) (7,16) (7,26) (18,24) (3,21) (0,1) (4,23) (6,2) (7,14) (23,2) (0,10) (23,11) (9,3) (0,17) (7,8) (21,23) (2,25) (4,15) (8,12) (20,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph772",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,11) (7,10) (31,17) (18,6) (16,10) (4,30) (20,17) (26,19) (13,1) (1,14) (18,2) (22,4) (28,21) (12,18) (20,25) (21,18) (7,14) (3,26) (9,24) (6,0) (32,23) (20,6) (32,2) (7,5) (4,6) (27,22) (32,7) (24,25) (29,10) (15,0) (24,19) (14,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph906",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (29,22) (2,18) (32,4) (9,7) (7,32) (2,34) (17,33) (14,13) (12,11) (25,20) (26,3) (21,18) (21,30) (24,25) (0,23) (6,4) (32,27) (34,8) (19,24) (0,6) (20,17) (15,18) (10,7) (19,28) (20,6) (4,22) (10,31) (18,6) (10,26) (16,1) (1,14) (14,7) (11,24) (5,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph284",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (25,17) (23,18) (21,27) (26,0) (9,11) (7,0) (19,0) (21,16) (15,12) (22,13) (18,10) (9,17) (24,9) (2,3) (25,15) (20,2) (14,6) (8,4) (7,1) (27,4) (14,0) (5,24) (19,20) (15,22) (10,21) (5,23) (12,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1698",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,17) (6,10) (25,22) (4,29) (7,23) (9,15) (18,28) (21,13) (8,7) (6,31) (0,31) (3,10) (9,11) (30,14) (1,22) (25,11) (18,27) (16,7) (3,4) (24,13) (19,2) (4,7) (2,7) (18,21) (23,20) (5,22) (10,26) (30,13) (0,2) (5,12) (25,14) (30,4) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph464",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,14) (15,16) (15,27) (6,5) (18,11) (16,0) (2,10) (16,19) (17,21) (11,5) (20,8) (5,21) (3,26) (24,0) (14,9) (4,18) (15,28) (29,1) (22,5) (29,24) (23,0) (8,25) (5,20) (12,7) (28,9) (7,28) (3,0) (5,27) (26,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1607",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,31) (0,21) (12,15) (31,9) (7,27) (30,17) (18,29) (25,12) (20,7) (30,13) (16,19) (18,22) (10,15) (24,16) (1,11) (8,31) (28,3) (31,12) (11,15) (15,5) (20,11) (23,29) (14,11) (0,1) (16,0) (4,21) (19,13) (10,28) (16,26) (7,2) (12,23) (12,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1571",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,10) (11,9) (22,30) (16,12) (22,20) (5,27) (30,19) (8,14) (17,25) (15,25) (2,0) (27,7) (26,2) (1,0) (24,6) (2,28) (1,13) (4,13) (26,1) (12,1) (4,14) (21,20) (1,18) (0,15) (3,27) (15,6) (4,11) (17,9) (29,6) (9,5) (25,20) (23,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1735",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (3,32) (2,22) (10,8) (14,29) (23,24) (26,18) (10,30) (8,16) (0,27) (17,14) (15,0) (22,11) (20,28) (11,19) (2,13) (24,32) (12,26) (17,1) (31,26) (17,31) (7,26) (2,7) (10,4) (0,21) (30,31) (5,3) (28,25) (0,1) (10,28) (15,4) (9,23) (24,2) (6,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph236",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,18) (21,8) (0,3) (14,7) (15,16) (20,8) (12,9) (22,3) (24,27) (2,6) (13,11) (0,19) (9,21) (5,11) (5,4) (15,25) (16,0) (14,16) (10,7) (15,23) (26,27) (20,5) (5,27) (18,5) (5,17) (2,26) (24,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph199",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,9) (23,26) (7,26) (12,2) (18,21) (14,15) (8,19) (24,17) (0,10) (4,24) (3,13) (16,6) (0,6) (24,3) (6,25) (26,16) (26,5) (18,22) (21,23) (9,1) (18,9) (18,3) (1,15) (1,8) (20,12) (13,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1690",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,24) (10,3) (26,15) (17,20) (29,0) (10,12) (21,29) (17,16) (8,14) (13,22) (28,7) (12,0) (2,0) (17,15) (6,19) (9,28) (13,11) (4,20) (25,20) (22,17) (16,27) (7,19) (2,8) (7,5) (23,28) (26,9) (0,1) (18,11) (28,14) (30,2) (3,31) (1,7) (27,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1531",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (27,2) (16,8) (28,6) (14,13) (18,25) (17,29) (23,30) (25,21) (21,12) (14,6) (9,12) (15,1) (24,26) (25,24) (4,20) (3,20) (22,26) (13,27) (6,23) (29,11) (20,19) (0,4) (3,0) (0,1) (22,29) (2,4) (8,22) (24,20) (19,7) (6,0) (3,5) (15,0) (10,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph92",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,4) (18,9) (1,12) (5,21) (13,25) (1,7) (4,12) (7,8) (20,7) (15,18) (16,8) (14,15) (1,10) (2,22) (20,25) (13,0) (6,9) (17,25) (2,21) (0,23) (25,24) (14,10) (25,19) (5,4) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph989",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (28,3) (26,3) (0,22) (5,4) (16,20) (4,13) (16,17) (5,27) (31,4) (25,23) (10,12) (14,33) (30,1) (7,18) (28,22) (32,15) (0,30) (29,11) (21,8) (25,34) (4,12) (25,6) (24,23) (6,9) (11,15) (31,15) (30,16) (33,9) (16,8) (21,14) (21,19) (34,18) (17,2) (26,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1727",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,15) (10,2) (30,5) (3,27) (31,9) (24,22) (26,24) (29,16) (15,4) (27,8) (17,20) (17,12) (1,2) (14,31) (1,0) (8,29) (25,2) (6,0) (3,0) (0,2) (31,11) (28,32) (8,23) (29,7) (21,23) (4,20) (26,18) (11,19) (2,26) (16,18) (13,0) (29,15) (22,30) (23,19) (10,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph933",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,1) (7,24) (28,26) (9,30) (1,30) (32,27) (2,7) (1,26) (3,16) (32,6) (31,4) (12,21) (17,0) (33,31) (3,11) (34,8) (26,22) (29,22) (25,17) (10,11) (14,19) (8,18) (4,15) (5,29) (27,31) (29,13) (5,12) (19,33) (20,32) (16,25) (22,18) (16,12) (11,27) (23,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph916",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,12) (27,28) (9,11) (32,14) (25,5) (10,23) (6,17) (14,5) (27,5) (15,24) (19,30) (17,20) (29,17) (8,22) (2,30) (21,25) (31,21) (3,32) (24,0) (13,3) (3,1) (13,29) (12,4) (9,0) (16,0) (14,22) (7,33) (4,32) (23,26) (18,23) (28,9) (10,21) (1,33) (34,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1283",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,9) (11,8) (16,7) (15,4) (11,17) (25,24) (9,25) (3,13) (1,7) (12,0) (0,3) (20,2) (23,1) (10,9) (19,15) (17,16) (0,1) (26,3) (6,7) (4,2) (26,5) (2,0) (12,17) (5,24) (27,8) (24,22) (8,3) (23,14) (18,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1123",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,3) (13,26) (2,11) (2,15) (19,17) (16,11) (22,16) (1,3) (4,17) (8,19) (10,15) (23,12) (14,20) (1,0) (11,25) (11,6) (18,19) (7,20) (19,10) (2,0) (21,9) (5,2) (17,13) (25,7) (9,2) (12,13) (3,0) (24,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1630",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,11) (21,3) (19,13) (9,10) (12,10) (11,24) (22,18) (0,20) (28,14) (23,14) (8,26) (11,19) (19,25) (2,0) (6,30) (1,7) (27,1) (1,0) (31,18) (29,2) (28,15) (28,1) (3,0) (4,8) (4,13) (15,30) (17,18) (24,14) (24,5) (9,28) (27,22) (0,16) (21,29) (22,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph860",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (3,16) (9,17) (19,8) (3,10) (24,16) (8,22) (23,27) (3,25) (13,29) (32,25) (20,31) (29,28) (2,1) (9,33) (8,30) (12,14) (13,0) (30,6) (10,2) (22,32) (21,3) (14,23) (22,18) (8,14) (4,29) (32,20) (11,23) (7,33) (1,15) (5,32) (26,10) (28,12) (21,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1143",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,20) (15,8) (1,0) (21,6) (0,21) (1,15) (0,2) (16,5) (0,17) (19,22) (26,11) (7,17) (16,11) (14,4) (23,14) (3,21) (12,0) (24,22) (10,4) (20,25) (19,4) (19,21) (13,12) (8,2) (9,11) (11,14) (25,7) (18,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph41",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,10) (15,16) (7,2) (0,19) (9,21) (2,6) (0,16) (1,18) (15,22) (9,12) (4,5) (25,10) (5,20) (5,18) (14,16) (0,3) (11,5) (5,17) (21,8) (15,23) (14,7) (0,24) (20,8) (5,3) (11,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1928",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,14) (3,10) (25,11) (10,19) (11,9) (20,2) (21,31) (25,23) (10,27) (29,18) (26,14) (12,5) (28,18) (22,1) (8,7) (7,24) (17,7) (7,2) (7,4) (22,23) (0,1) (13,21) (10,6) (5,6) (9,16) (4,32) (0,31) (30,4) (5,33) (4,3) (30,13) (34,18) (13,25) (15,22) (5,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1850",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (26,5) (28,5) (31,27) (15,14) (9,29) (13,20) (23,13) (23,12) (24,22) (2,16) (1,0) (0,2) (19,28) (22,30) (24,23) (0,5) (21,32) (24,19) (3,0) (18,13) (24,25) (16,13) (4,25) (7,28) (27,11) (5,29) (24,11) (3,10) (10,16) (33,2) (21,11) (11,1) (31,17) (8,29) (29,6) (12,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph60",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,11) (17,24) (24,20) (9,17) (3,7) (16,8) (21,0) (4,14) (14,0) (10,2) (15,9) (19,18) (0,18) (1,12) (22,7) (12,5) (21,7) (25,10) (13,22) (8,12) (24,4) (10,23) (23,4) (6,5) (12,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph918",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,5) (17,1) (32,9) (2,16) (33,4) (7,5) (24,11) (12,27) (30,13) (32,28) (12,14) (30,32) (8,15) (19,7) (20,7) (0,25) (31,1) (11,21) (6,12) (24,29) (10,12) (15,9) (13,14) (26,11) (34,12) (21,20) (0,17) (5,4) (22,18) (23,15) (16,34) (3,20) (16,31) (18,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1532",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,27) (3,14) (12,22) (0,2) (20,5) (21,9) (0,5) (27,24) (13,29) (10,15) (17,15) (0,3) (19,18) (15,2) (18,2) (16,23) (1,8) (18,9) (13,15) (30,17) (14,6) (16,7) (16,12) (8,13) (13,0) (17,11) (6,16) (8,25) (24,26) (1,0) (3,4) (5,14) (11,28) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1638",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,25) (8,25) (29,1) (6,13) (18,25) (14,1) (3,0) (22,17) (1,27) (9,27) (24,10) (18,12) (31,2) (4,19) (20,13) (21,10) (11,5) (31,15) (28,21) (20,28) (29,22) (0,5) (26,0) (8,9) (20,31) (0,2) (21,18) (23,21) (11,21) (20,7) (1,0) (16,22) (30,18) (3,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1273",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,27) (3,0) (16,1) (6,25) (15,8) (3,25) (9,2) (21,4) (5,18) (10,24) (4,17) (2,0) (23,6) (24,0) (23,21) (11,22) (7,26) (27,23) (10,11) (15,18) (24,12) (18,19) (0,1) (14,8) (2,15) (25,15) (20,24) (13,26) (8,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph979",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,34) (23,4) (7,32) (8,2) (32,23) (29,13) (20,9) (29,6) (24,16) (28,19) (12,33) (23,27) (18,23) (5,1) (33,2) (0,32) (17,27) (26,4) (18,24) (14,6) (4,21) (32,13) (10,23) (5,3) (18,15) (31,0) (0,33) (11,28) (26,30) (5,26) (28,2) (25,27) (4,34) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph4",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,22) (23,20) (2,25) (5,13) (16,9) (20,0) (5,4) (16,13) (15,10) (18,1) (12,14) (11,14) (19,4) (25,21) (0,14) (24,1) (17,12) (0,7) (17,1) (8,3) (23,8) (11,5) (15,11) (7,2) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph205",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,20) (22,3) (23,27) (2,12) (20,1) (15,0) (2,19) (18,9) (27,9) (1,19) (16,2) (15,17) (23,25) (23,24) (4,8) (13,6) (3,0) (8,25) (7,15) (8,11) (25,21) (2,4) (8,5) (10,0) (9,13) (9,3) (10,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph391",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,5) (17,20) (7,0) (26,19) (17,3) (14,23) (9,11) (16,28) (22,12) (2,0) (19,15) (19,9) (20,4) (16,24) (20,12) (0,14) (7,25) (1,12) (19,16) (5,2) (2,4) (25,10) (26,27) (6,21) (1,8) (26,18) (13,0) (8,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1282",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,22) (0,6) (5,12) (19,6) (13,20) (18,14) (5,11) (23,2) (24,14) (3,4) (1,3) (24,12) (1,0) (20,17) (26,6) (4,23) (4,25) (13,7) (7,15) (22,6) (4,16) (8,17) (4,19) (26,5) (21,6) (27,7) (0,13) (19,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph388",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (19,6) (11,12) (12,22) (9,15) (28,27) (19,16) (3,12) (0,27) (11,19) (13,20) (21,28) (18,4) (13,9) (2,1) (25,23) (24,0) (23,5) (26,18) (10,15) (10,17) (5,16) (20,3) (1,11) (7,14) (16,7) (28,20) (26,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1410",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,26) (28,3) (2,11) (29,0) (11,13) (12,11) (25,5) (7,15) (14,28) (18,5) (0,2) (20,4) (1,18) (29,8) (15,3) (5,4) (25,24) (2,16) (19,21) (17,28) (1,0) (3,23) (27,17) (26,19) (29,12) (1,19) (23,10) (27,6) (12,22) (21,3) (18,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph402",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,16) (24,0) (29,24) (9,28) (5,20) (26,2) (5,22) (27,5) (12,7) (19,16) (23,0) (5,6) (11,5) (0,3) (7,28) (18,11) (21,17) (21,5) (1,29) (14,9) (2,10) (27,15) (20,8) (16,0) (4,18) (28,15) (3,26) (14,13) (25,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph344",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,16) (13,23) (17,19) (20,27) (9,5) (9,11) (26,16) (2,13) (0,7) (7,12) (21,17) (27,28) (18,22) (6,9) (25,16) (8,27) (12,26) (10,25) (15,22) (5,24) (24,23) (25,4) (0,3) (20,10) (11,14) (22,3) (8,21) (8,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1718",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,11) (2,1) (2,12) (0,1) (5,0) (0,3) (30,24) (10,11) (25,18) (6,10) (29,23) (13,9) (23,5) (10,27) (32,25) (15,31) (19,7) (17,26) (32,19) (0,4) (20,32) (28,23) (20,29) (4,5) (11,20) (17,2) (8,16) (13,10) (24,27) (22,28) (14,15) (14,1) (0,2) (3,5) (27,16) (23,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1736",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,10) (32,26) (15,19) (1,24) (18,24) (5,9) (14,4) (24,20) (19,18) (17,6) (4,27) (1,11) (22,0) (13,20) (6,28) (5,3) (10,19) (1,0) (9,0) (22,2) (13,31) (21,6) (0,2) (9,27) (17,22) (23,16) (23,12) (24,3) (25,21) (29,23) (3,16) (1,7) (32,13) (14,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph32",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,9) (10,21) (21,20) (2,20) (18,0) (7,15) (15,14) (24,21) (9,13) (12,16) (19,18) (15,16) (16,19) (20,8) (13,25) (6,8) (3,20) (17,11) (5,20) (16,23) (5,17) (10,22) (1,5) (7,4) (9,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph713",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,5) (13,9) (20,22) (30,12) (6,1) (3,32) (16,26) (18,20) (2,0) (16,9) (29,24) (7,29) (18,11) (12,23) (15,16) (6,4) (6,14) (32,25) (24,4) (25,27) (26,1) (20,19) (8,25) (7,12) (26,31) (1,19) (28,4) (2,7) (6,27) (10,22) (21,17) (6,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1173",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,17) (7,23) (26,15) (11,9) (14,25) (11,12) (6,1) (14,20) (8,14) (13,19) (12,21) (8,23) (5,6) (22,25) (0,2) (3,0) (15,6) (5,0) (4,0) (16,6) (9,18) (3,18) (15,0) (24,19) (6,4) (0,1) (13,9) (20,10) (18,2) (25,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph69",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,22) (14,5) (2,11) (9,6) (3,24) (1,2) (0,7) (13,10) (23,13) (4,8) (15,22) (24,6) (2,18) (16,8) (25,4) (7,4) (18,5) (19,0) (12,19) (11,17) (22,9) (4,20) (2,10) (21,10) (14,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph118",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,2) (8,10) (16,3) (16,17) (4,24) (17,6) (26,7) (1,25) (12,3) (15,2) (23,12) (13,25) (10,23) (20,19) (5,0) (14,26) (26,9) (0,11) (22,26) (0,24) (24,16) (3,26) (23,18) (13,14) (21,23) (20,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph101",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,25) (26,11) (15,16) (23,13) (22,13) (18,9) (2,5) (8,5) (3,26) (11,15) (6,9) (13,9) (12,21) (19,20) (24,0) (13,7) (1,17) (10,0) (17,8) (21,8) (14,11) (19,26) (11,13) (17,0) (23,0) (3,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph509",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,28) (13,6) (22,8) (14,20) (24,29) (27,11) (19,23) (15,30) (17,22) (10,22) (5,18) (12,30) (18,24) (11,2) (23,9) (13,23) (11,14) (4,13) (1,25) (21,5) (16,3) (10,19) (26,21) (1,19) (20,0) (18,12) (3,2) (7,24) (11,10) (9,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph437",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,2) (28,25) (23,5) (29,10) (25,15) (7,14) (22,14) (28,17) (26,15) (11,4) (18,23) (17,9) (24,9) (12,15) (22,26) (19,0) (13,9) (10,18) (1,7) (0,16) (0,29) (21,20) (8,0) (27,12) (20,6) (27,4) (24,5) (29,2) (19,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph384",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,13) (9,4) (22,4) (7,17) (4,24) (6,24) (5,3) (3,15) (16,14) (8,12) (22,19) (1,4) (15,0) (10,21) (23,14) (26,1) (4,12) (20,24) (13,28) (3,17) (23,17) (23,25) (27,21) (7,18) (11,1) (21,1) (2,0) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1854",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,19) (8,12) (9,15) (2,33) (1,6) (22,20) (13,33) (7,29) (4,30) (18,6) (20,19) (11,22) (25,20) (26,32) (23,17) (29,24) (16,21) (2,0) (1,0) (10,25) (16,26) (6,17) (0,3) (7,3) (27,33) (7,12) (14,18) (12,28) (4,0) (6,27) (9,16) (4,24) (4,6) (1,26) (32,5) (12,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph594",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,22) (26,24) (15,7) (18,30) (12,5) (17,10) (6,9) (7,28) (1,15) (17,22) (14,9) (29,27) (12,25) (15,26) (26,21) (8,10) (20,18) (11,8) (0,20) (5,7) (30,13) (29,23) (6,2) (19,8) (20,29) (26,11) (16,2) (23,2) (26,2) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1175",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,0) (5,11) (4,3) (9,19) (6,20) (5,26) (0,6) (4,24) (6,19) (19,4) (16,20) (5,12) (6,21) (24,14) (0,1) (7,4) (15,7) (17,14) (13,18) (2,23) (17,8) (22,10) (13,26) (3,1) (12,23) (6,25) (4,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1330",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,12) (6,25) (20,14) (13,5) (0,5) (20,2) (23,26) (21,15) (17,24) (26,3) (24,28) (7,11) (0,4) (10,26) (3,21) (26,9) (2,0) (14,15) (18,16) (23,25) (0,18) (11,0) (28,26) (8,11) (19,17) (6,0) (1,0) (3,0) (22,1) (1,13) (8,27) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1174",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,19) (26,20) (17,10) (8,10) (6,9) (23,2) (12,5) (20,23) (15,26) (11,26) (25,2) (26,21) (2,6) (11,8) (14,2) (8,4) (16,8) (7,24) (15,1) (7,15) (9,13) (7,5) (20,0) (1,0) (18,26) (3,22) (12,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph874",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (30,31) (1,4) (31,22) (29,27) (8,10) (7,32) (17,33) (6,20) (1,13) (0,20) (27,12) (13,28) (32,25) (32,21) (6,21) (8,4) (2,8) (12,11) (5,19) (13,14) (4,27) (14,23) (18,21) (6,15) (3,18) (3,8) (30,9) (10,31) (19,9) (16,10) (26,9) (24,32) (17,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1861",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,31) (33,18) (23,1) (16,15) (26,10) (2,4) (4,21) (20,30) (33,28) (29,13) (1,27) (23,4) (28,12) (32,29) (0,1) (29,25) (19,3) (18,14) (7,24) (15,9) (23,8) (19,8) (8,24) (13,0) (17,11) (13,20) (30,33) (10,22) (11,29) (26,32) (0,2) (6,16) (6,31) (27,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph718",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,23) (23,15) (10,16) (30,17) (14,31) (10,29) (17,21) (9,19) (1,27) (17,7) (27,22) (11,3) (31,22) (22,13) (0,27) (4,17) (0,25) (29,26) (29,28) (2,13) (1,24) (7,6) (26,2) (4,23) (1,12) (19,18) (11,27) (8,5) (5,19) (27,20) (16,8) (30,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1203",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,0) (10,3) (16,11) (8,2) (0,10) (6,2) (24,27) (26,4) (0,4) (7,19) (6,17) (25,22) (5,16) (1,19) (24,15) (18,8) (6,16) (13,4) (20,16) (0,2) (23,0) (22,16) (24,14) (12,8) (1,21) (3,0) (9,25) (1,0) (6,19) (11,26) (26,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1667",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,23) (19,30) (14,5) (0,2) (9,1) (21,17) (28,9) (27,15) (12,29) (2,18) (26,25) (29,27) (22,10) (0,24) (20,17) (14,25) (26,3) (23,13) (23,1) (8,6) (6,16) (10,2) (4,11) (30,6) (22,20) (16,31) (23,4) (27,7) (21,19) (31,5) (30,9) (0,1) (0,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph419",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,20) (12,24) (27,7) (27,21) (14,9) (15,23) (16,10) (5,24) (21,2) (26,3) (29,28) (9,17) (8,7) (6,20) (25,12) (23,12) (0,3) (19,1) (3,8) (7,11) (18,23) (16,8) (4,22) (29,24) (8,13) (14,21) (27,28) (22,9) (2,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph845",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (3,4) (22,15) (18,21) (22,1) (31,0) (16,9) (4,7) (24,7) (31,4) (30,14) (10,27) (6,10) (25,13) (5,32) (7,2) (30,4) (20,2) (21,13) (7,17) (19,10) (7,8) (28,18) (10,3) (5,33) (23,22) (29,18) (5,6) (13,30) (25,11) (5,12) (25,23) (26,14) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph94",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,0) (15,18) (6,7) (22,3) (25,23) (22,8) (19,5) (15,9) (3,1) (13,15) (10,3) (20,17) (7,12) (16,10) (21,2) (16,21) (14,4) (20,6) (9,14) (10,11) (15,5) (8,6) (14,8) (21,24) (24,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph604",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (14,7) (19,23) (3,26) (30,17) (14,1) (0,15) (20,25) (7,4) (22,31) (26,22) (20,17) (6,0) (10,29) (10,7) (4,27) (16,10) (19,24) (12,18) (22,2) (18,6) (18,21) (6,4) (11,8) (28,21) (25,24) (13,1) (7,5) (11,14) (2,18) (6,20) (9,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1108",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,17) (19,25) (20,21) (25,2) (16,15) (1,0) (26,10) (8,25) (10,20) (13,25) (4,18) (22,3) (11,18) (26,24) (5,15) (1,16) (9,25) (26,5) (3,18) (13,0) (14,21) (18,21) (12,8) (2,18) (17,7) (6,17) (16,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1089",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,15) (24,20) (2,23) (14,25) (1,7) (3,9) (13,10) (16,8) (23,11) (17,4) (16,14) (23,21) (16,0) (18,15) (12,21) (0,9) (24,17) (22,8) (6,10) (24,22) (6,14) (24,5) (11,19) (1,15) (4,19) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph544",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,5) (20,12) (27,7) (19,16) (0,7) (17,3) (24,16) (21,6) (5,2) (20,17) (12,22) (9,11) (29,25) (8,1) (29,26) (8,6) (14,0) (14,23) (30,16) (25,10) (0,13) (18,26) (15,19) (4,2) (26,28) (9,19) (19,26) (12,1) (20,4) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph229",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,24) (5,16) (0,16) (4,1) (9,21) (0,26) (23,4) (20,6) (22,27) (10,1) (13,20) (11,24) (11,8) (18,4) (18,3) (23,16) (8,23) (1,20) (12,7) (21,15) (19,22) (19,6) (9,7) (14,26) (6,17) (25,14) (2,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1074",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (12,3) (19,6) (9,15) (2,0) (25,23) (0,23) (0,1) (20,13) (12,24) (20,3) (21,0) (11,12) (5,22) (15,10) (4,18) (23,20) (7,16) (8,0) (1,11) (2,1) (16,19) (16,5) (18,12) (10,17) (9,13) (0,3) (14,7) (19,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph917",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,17) (22,5) (8,31) (33,13) (12,1) (3,10) (13,0) (4,8) (23,7) (16,2) (10,34) (6,23) (26,27) (9,33) (30,28) (24,10) (18,7) (0,15) (25,13) (20,15) (11,24) (24,21) (8,0) (14,15) (22,34) (28,8) (19,30) (10,13) (29,1) (4,29) (17,11) (6,15) (3,16) (32,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph956",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,2) (3,33) (26,2) (11,5) (7,19) (14,24) (32,30) (29,0) (19,10) (21,32) (32,27) (9,6) (16,28) (8,5) (30,15) (5,1) (27,12) (25,22) (5,32) (9,11) (19,24) (24,3) (0,31) (34,17) (14,2) (34,25) (29,14) (34,12) (20,23) (13,22) (12,4) (5,14) (27,20) (18,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1135",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (19,11) (20,8) (10,2) (5,0) (18,24) (6,23) (1,26) (13,17) (7,22) (9,24) (10,20) (20,14) (15,16) (0,1) (12,15) (0,24) (11,3) (17,4) (1,6) (18,6) (16,9) (19,2) (22,13) (3,7) (18,8) (25,0) (21,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1418",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,27) (29,16) (10,3) (27,28) (12,25) (18,11) (24,13) (24,7) (24,21) (10,14) (15,27) (18,21) (19,18) (24,14) (23,21) (17,7) (26,4) (0,2) (6,7) (1,0) (7,22) (0,3) (6,0) (11,20) (17,12) (8,28) (29,19) (1,22) (3,5) (6,9) (19,2) (26,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1535",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,26) (23,1) (28,7) (23,14) (6,14) (27,11) (8,28) (22,29) (25,29) (15,29) (16,18) (3,27) (19,2) (8,4) (23,19) (13,15) (5,30) (0,27) (0,21) (24,1) (2,0) (6,9) (14,20) (10,16) (4,29) (23,28) (22,12) (0,1) (23,11) (17,22) (11,16) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph350",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,13) (12,20) (18,1) (27,28) (5,14) (27,23) (21,5) (13,5) (19,6) (21,18) (2,11) (6,26) (19,1) (12,25) (27,0) (27,3) (21,17) (9,24) (23,15) (25,23) (2,7) (1,4) (16,25) (27,22) (19,8) (10,2) (26,11) (9,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1320",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (28,26) (1,8) (25,3) (13,16) (12,22) (7,10) (10,6) (14,23) (8,14) (0,4) (7,9) (2,0) (0,1) (19,5) (2,3) (5,22) (25,16) (2,23) (20,6) (9,26) (15,14) (24,11) (11,13) (1,21) (18,24) (17,27) (17,3) (0,3) (12,23) (4,14) (20,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph89",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (3,5) (11,17) (24,5) (18,12) (2,20) (23,14) (12,17) (24,8) (25,9) (22,24) (25,3) (10,9) (15,19) (7,16) (15,4) (1,23) (9,21) (3,13) (8,11) (7,6) (1,7) (2,4) (0,12) (17,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph302",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,23) (22,2) (27,25) (3,12) (16,27) (9,26) (20,9) (23,12) (23,21) (17,6) (24,28) (11,0) (14,13) (3,26) (20,19) (3,16) (4,24) (24,0) (28,14) (25,1) (15,2) (5,0) (10,8) (22,26) (13,26) (17,16) (23,10) (7,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph529",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (25,23) (25,17) (9,3) (29,24) (28,14) (0,13) (7,8) (25,20) (2,21) (27,5) (12,1) (8,16) (28,10) (7,1) (18,9) (21,27) (4,5) (9,6) (15,14) (28,0) (19,10) (7,20) (11,4) (28,25) (13,30) (2,29) (22,1) (4,12) (27,26) (18,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph347",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,12) (1,9) (0,6) (23,7) (25,20) (4,28) (14,6) (3,18) (2,7) (25,5) (1,5) (23,11) (26,22) (16,26) (18,19) (24,8) (27,4) (15,21) (27,13) (16,15) (1,11) (2,10) (14,26) (13,1) (8,20) (17,15) (10,15) (18,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1030",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,14) (21,8) (25,9) (10,4) (13,0) (11,24) (10,15) (17,20) (6,25) (1,0) (2,3) (22,5) (21,7) (15,18) (6,13) (1,23) (18,14) (19,3) (3,4) (5,0) (12,4) (2,24) (23,13) (16,8) (21,18) (10,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1586",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (22,17) (11,9) (28,0) (11,15) (25,16) (12,7) (13,2) (3,24) (0,1) (7,0) (3,29) (13,23) (5,9) (18,22) (6,9) (23,26) (16,1) (8,21) (25,4) (12,26) (27,30) (29,16) (8,27) (10,25) (24,5) (21,17) (22,19) (2,0) (14,30) (20,27) (13,8) (10,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph142",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,23) (9,1) (3,14) (24,13) (20,25) (10,22) (5,22) (11,8) (21,3) (11,18) (16,0) (11,19) (9,21) (19,15) (17,19) (4,14) (6,24) (18,25) (13,12) (26,12) (2,1) (13,16) (4,7) (14,19) (15,22) (17,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1556",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,12) (10,21) (27,23) (8,15) (18,19) (5,11) (15,13) (0,4) (17,20) (0,23) (30,3) (7,13) (2,0) (17,14) (4,22) (25,24) (1,0) (18,7) (21,27) (24,29) (23,8) (16,22) (14,10) (5,17) (25,3) (3,0) (28,11) (14,1) (3,16) (26,19) (30,2) (23,6) (20,24) (9,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph109",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,9) (2,11) (0,19) (0,20) (22,2) (24,12) (25,5) (10,5) (12,14) (10,9) (6,7) (20,10) (11,15) (16,0) (6,25) (1,15) (25,17) (22,18) (5,3) (11,23) (17,4) (21,15) (10,14) (2,26) (8,10) (16,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph200",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,13) (7,25) (21,19) (27,6) (3,21) (8,6) (5,20) (6,26) (14,4) (7,23) (0,23) (10,19) (24,17) (15,1) (1,12) (17,11) (16,19) (2,6) (22,13) (5,16) (13,9) (22,27) (23,1) (20,13) (24,21) (18,15) (24,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1494",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,27) (0,24) (11,14) (22,3) (9,11) (29,3) (0,7) (13,23) (1,16) (1,0) (16,28) (9,6) (13,8) (17,19) (22,15) (5,9) (25,16) (20,10) (27,20) (26,12) (7,12) (4,25) (21,17) (10,25) (2,13) (18,22) (27,29) (24,5) (26,23) (21,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph900",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (27,17) (11,28) (27,23) (13,32) (22,34) (24,16) (5,26) (2,33) (9,3) (34,4) (15,18) (4,26) (19,28) (8,2) (31,0) (6,14) (1,5) (10,23) (32,23) (0,32) (18,24) (21,4) (30,26) (23,18) (23,4) (29,6) (25,27) (2,28) (7,32) (13,29) (12,33) (3,5) (20,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph568",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,17) (8,12) (0,1) (17,25) (7,14) (5,20) (28,2) (18,13) (3,24) (2,6) (1,13) (16,7) (7,8) (22,6) (18,27) (16,19) (29,7) (23,11) (9,3) (22,20) (4,15) (3,21) (20,30) (17,0) (26,2) (0,10) (23,28) (21,23) (19,0) (23,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1258",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,0) (17,21) (23,2) (20,23) (11,8) (22,3) (0,1) (0,20) (18,27) (12,24) (26,11) (2,26) (1,15) (5,12) (9,6) (17,10) (16,8) (2,14) (9,13) (7,15) (8,10) (26,15) (8,4) (3,0) (5,7) (26,19) (25,7) (6,2) (22,26) (18,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1779",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,9) (29,14) (1,0) (31,14) (14,32) (8,26) (13,14) (20,0) (4,21) (29,17) (10,0) (22,10) (9,24) (18,27) (23,30) (3,20) (1,12) (28,14) (27,4) (26,7) (14,6) (5,12) (30,8) (14,16) (27,30) (22,7) (2,0) (7,19) (28,25) (0,24) (2,6) (29,11) (24,15) (22,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,14) (9,11) (9,18) (17,1) (25,14) (8,14) (13,9) (2,18) (0,3) (6,5) (0,15) (25,6) (7,23) (23,8) (6,16) (6,4) (20,10) (24,19) (19,13) (11,12) (21,12) (6,1) (25,22) (15,6) (18,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph536",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,1) (30,21) (29,6) (26,24) (15,14) (9,22) (21,0) (14,4) (27,9) (15,7) (0,1) (28,2) (19,7) (23,24) (1,16) (9,20) (8,12) (13,18) (5,30) (11,3) (6,11) (10,2) (10,25) (26,14) (7,10) (13,26) (17,25) (12,9) (9,7) (29,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1761",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (26,9) (2,0) (16,8) (1,19) (3,1) (20,7) (32,23) (2,23) (18,24) (27,23) (6,31) (9,27) (10,1) (29,32) (30,11) (32,15) (16,25) (14,15) (9,24) (11,27) (4,14) (22,6) (3,0) (8,28) (5,32) (13,18) (14,31) (23,10) (0,4) (24,8) (27,17) (25,21) (12,30) (20,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph951",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,30) (23,32) (21,16) (30,34) (21,17) (3,18) (29,8) (33,14) (7,8) (7,31) (14,6) (29,4) (9,28) (5,32) (27,10) (12,24) (14,25) (10,33) (29,11) (1,18) (8,22) (25,28) (28,30) (22,23) (26,2) (20,4) (16,7) (28,15) (19,14) (27,18) (14,23) (0,26) (13,33) (2,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph469",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,25) (18,3) (19,10) (28,20) (7,4) (12,0) (2,7) (21,17) (14,5) (25,11) (20,22) (23,29) (29,13) (23,21) (2,26) (24,11) (4,9) (22,16) (8,7) (14,15) (3,23) (5,19) (13,28) (0,19) (29,6) (29,5) (1,10) (1,8) (27,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1158",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,6) (22,2) (4,8) (17,25) (2,26) (14,3) (18,6) (10,12) (4,11) (7,2) (0,1) (9,5) (20,16) (1,12) (14,1) (25,15) (0,15) (2,0) (19,6) (3,0) (13,1) (6,15) (25,20) (1,23) (9,11) (26,20) (5,21) (13,4) (9,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1919",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,33) (34,12) (0,3) (2,12) (28,6) (0,23) (30,27) (27,22) (5,0) (15,16) (3,13) (14,0) (18,1) (16,20) (31,22) (5,16) (16,27) (14,10) (22,21) (1,0) (23,26) (27,29) (8,1) (9,12) (0,20) (4,18) (11,24) (4,29) (25,32) (11,1) (17,4) (24,7) (25,6) (0,2) (17,19) (32,19) (13,25) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1676",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,12) (16,20) (8,22) (20,21) (25,27) (0,2) (6,27) (10,18) (30,26) (22,12) (17,6) (15,26) (20,19) (1,6) (9,16) (29,24) (16,14) (18,17) (23,4) (4,24) (3,0) (13,6) (31,25) (6,4) (7,12) (7,2) (0,1) (25,5) (12,3) (9,11) (1,26) (1,19) (29,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph157",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (19,24) (9,10) (15,12) (22,26) (26,21) (8,17) (10,6) (10,0) (25,23) (12,16) (20,24) (11,23) (15,26) (9,21) (14,4) (3,14) (7,9) (21,14) (1,16) (11,7) (0,17) (0,19) (13,17) (5,18) (5,4) (26,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph908",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,10) (16,2) (32,33) (30,6) (28,9) (21,19) (33,27) (27,29) (26,31) (34,23) (20,17) (30,19) (1,32) (26,3) (24,23) (10,22) (14,25) (34,6) (0,15) (14,5) (31,15) (20,18) (17,21) (25,22) (29,12) (23,4) (5,33) (24,0) (13,23) (30,9) (27,7) (8,6) (11,4) (9,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph698",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,8) (17,14) (15,4) (29,18) (27,1) (12,0) (28,8) (14,7) (29,15) (8,12) (4,6) (0,31) (30,11) (5,11) (3,8) (26,19) (25,12) (22,13) (23,10) (17,11) (28,14) (9,13) (26,6) (1,26) (20,8) (21,13) (9,25) (10,8) (26,20) (2,7) (24,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1750",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (9,1) (6,16) (24,0) (23,13) (6,30) (9,30) (0,15) (10,22) (29,27) (28,9) (20,17) (15,27) (3,26) (8,6) (4,11) (23,4) (21,17) (2,18) (27,7) (5,31) (12,29) (25,14) (26,25) (5,14) (24,23) (2,0) (1,0) (21,19) (32,16) (20,22) (2,10) (19,30) (31,1) (23,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1601",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (20,22) (25,14) (1,0) (5,31) (21,19) (30,6) (30,9) (10,22) (14,5) (12,29) (6,16) (27,7) (26,25) (0,24) (4,11) (27,15) (10,2) (0,15) (6,8) (23,24) (9,1) (23,13) (2,18) (0,2) (30,19) (4,23) (16,31) (9,28) (17,20) (27,29) (17,21) (1,23) (26,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph34",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,3) (1,3) (12,5) (13,25) (20,16) (17,8) (0,6) (4,22) (19,6) (21,6) (4,7) (14,17) (22,10) (7,15) (18,13) (19,9) (6,24) (6,20) (11,5) (2,23) (14,24) (5,4) (23,12) (4,19) (13,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph87",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (24,21) (8,24) (12,25) (17,10) (1,23) (10,3) (14,4) (25,19) (19,7) (1,13) (5,13) (23,14) (4,8) (11,16) (22,23) (17,16) (20,1) (24,9) (15,21) (11,2) (6,3) (20,17) (16,7) (1,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1478",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,18) (7,19) (1,0) (7,4) (6,26) (8,2) (27,8) (11,10) (26,25) (3,9) (16,0) (6,10) (17,20) (12,7) (22,17) (15,28) (21,20) (26,14) (24,27) (26,0) (16,21) (23,19) (0,3) (0,2) (8,0) (17,4) (5,25) (6,29) (5,15) (15,9) (13,6) (1,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph945",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,34) (17,24) (28,11) (32,27) (31,7) (25,15) (18,22) (26,13) (28,7) (4,31) (1,16) (1,33) (10,29) (8,18) (2,31) (14,20) (32,22) (9,13) (28,16) (24,23) (4,25) (7,0) (8,12) (3,18) (15,26) (28,24) (4,8) (17,20) (5,2) (5,6) (29,20) (6,30) (6,19) (9,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1382",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,17) (25,4) (14,26) (1,9) (8,27) (13,9) (5,23) (24,15) (10,7) (22,25) (23,3) (19,17) (26,21) (25,7) (0,2) (9,8) (27,2) (25,18) (14,12) (6,13) (4,16) (22,11) (27,20) (28,5) (0,3) (1,0) (23,11) (16,14) (2,22) (15,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph800",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (33,10) (18,30) (11,4) (13,9) (19,32) (23,25) (27,0) (2,33) (16,1) (24,30) (1,2) (6,20) (12,18) (29,12) (5,21) (15,31) (4,13) (19,9) (31,0) (17,6) (7,21) (3,33) (28,12) (33,8) (20,21) (31,2) (3,22) (32,7) (28,5) (26,8) (7,10) (15,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1681",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,28) (4,29) (8,18) (9,12) (3,1) (31,9) (7,27) (25,6) (25,30) (29,7) (2,13) (5,25) (18,21) (3,19) (1,2) (26,29) (30,4) (21,28) (0,2) (23,9) (14,11) (8,1) (17,9) (4,15) (27,14) (5,20) (5,0) (2,10) (14,21) (0,3) (4,0) (24,23) (0,1) (20,16) (30,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1975",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,29) (18,6) (29,22) (2,0) (23,5) (26,14) (13,34) (27,10) (21,2) (12,17) (27,28) (24,4) (3,7) (28,30) (3,0) (10,31) (0,21) (1,0) (32,20) (15,10) (5,17) (9,23) (5,26) (10,29) (8,16) (4,32) (8,32) (15,3) (8,7) (18,13) (33,14) (17,13) (11,19) (2,24) (21,25) (0,11) (24,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1120",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,25) (20,17) (12,0) (25,16) (1,0) (23,22) (11,21) (8,15) (20,3) (24,19) (20,24) (2,13) (14,6) (15,1) (12,9) (7,19) (4,20) (25,24) (6,26) (26,22) (8,22) (21,6) (4,2) (17,10) (6,0) (3,5) (14,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1572",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,6) (4,18) (7,13) (3,0) (5,26) (27,12) (14,24) (2,7) (2,3) (9,4) (5,16) (13,0) (4,0) (0,6) (22,15) (6,29) (4,19) (10,17) (0,2) (23,8) (17,7) (24,6) (11,19) (25,4) (30,3) (21,20) (28,4) (12,5) (14,20) (1,3) (0,1) (23,6) (22,13) (26,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph847",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,27) (18,28) (17,5) (20,14) (33,3) (29,14) (5,1) (19,29) (11,16) (18,12) (24,19) (32,10) (20,22) (30,9) (7,25) (17,13) (33,13) (8,17) (26,25) (4,15) (22,16) (10,9) (21,1) (16,23) (10,0) (17,31) (23,33) (28,16) (2,6) (4,0) (7,4) (6,15) (7,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1398",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,10) (27,16) (27,25) (9,26) (14,13) (0,5) (24,28) (4,24) (0,1) (24,0) (25,1) (0,4) (21,23) (26,3) (26,7) (17,6) (2,22) (15,2) (12,23) (2,0) (17,16) (16,3) (20,9) (12,3) (23,18) (0,11) (10,23) (20,19) (26,13) (14,28) (0,3) (26,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1559",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,16) (18,8) (22,7) (24,9) (5,27) (3,7) (2,10) (18,24) (24,0) (6,18) (13,26) (0,28) (1,6) (11,19) (15,20) (0,14) (10,20) (1,0) (30,29) (27,6) (29,1) (25,17) (2,19) (29,17) (21,15) (12,17) (13,22) (11,3) (2,0) (4,30) (20,8) (23,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph579",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (18,2) (9,18) (6,14) (18,19) (13,15) (22,12) (27,0) (16,6) (8,13) (30,17) (25,8) (23,16) (24,26) (10,15) (0,3) (3,4) (9,21) (17,15) (11,17) (14,5) (3,14) (12,16) (5,20) (28,11) (2,15) (0,13) (13,29) (24,27) (16,7) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1730",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (2,17) (21,23) (5,3) (20,29) (2,1) (18,25) (24,30) (11,10) (23,29) (27,24) (20,11) (14,1) (22,28) (4,5) (19,32) (2,12) (15,14) (20,32) (23,5) (15,31) (28,23) (10,27) (17,26) (6,10) (3,0) (25,32) (11,1) (19,7) (16,8) (0,2) (9,13) (0,1) (27,16) (13,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph844",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (16,9) (28,18) (12,5) (6,10) (33,5) (31,4) (13,30) (21,13) (22,23) (0,31) (5,32) (2,20) (13,25) (4,30) (4,7) (4,3) (25,11) (23,25) (27,10) (15,22) (2,7) (14,26) (7,17) (21,18) (24,7) (5,6) (10,19) (18,29) (30,14) (7,8) (22,1) (3,10) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1000",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,25) (22,15) (6,4) (0,1) (9,4) (5,2) (11,15) (14,1) (13,23) (16,1) (17,24) (1,10) (20,16) (7,9) (22,8) (3,18) (10,21) (10,3) (19,0) (12,0) (11,19) (7,15) (17,0) (25,23) (6,2) (16,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1899",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,10) (31,2) (1,0) (9,3) (31,17) (12,16) (8,13) (12,13) (21,19) (25,11) (21,2) (12,28) (6,22) (5,2) (4,31) (30,12) (3,30) (8,32) (1,22) (24,19) (26,33) (27,0) (14,18) (23,22) (18,25) (25,10) (7,26) (20,2) (32,17) (12,26) (24,0) (4,15) (11,32) (23,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph786",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,30) (28,18) (0,7) (10,26) (9,26) (32,22) (16,22) (7,18) (5,15) (2,11) (17,8) (20,16) (16,14) (9,17) (19,2) (4,26) (30,24) (1,4) (11,20) (23,21) (17,6) (19,5) (31,12) (21,1) (4,27) (4,29) (19,7) (9,3) (31,13) (27,13) (25,0) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1709",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,29) (10,19) (15,21) (30,22) (2,3) (17,10) (8,6) (17,5) (4,27) (18,1) (20,10) (1,10) (24,10) (11,31) (14,9) (32,9) (25,7) (13,4) (1,0) (26,21) (10,11) (26,23) (12,10) (27,23) (16,3) (6,30) (2,26) (11,14) (7,9) (26,0) (2,17) (14,30) (29,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph288",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,5) (22,1) (9,23) (5,6) (14,27) (4,25) (26,7) (14,25) (21,9) (22,2) (24,22) (4,18) (23,26) (3,12) (19,22) (13,6) (14,0) (2,16) (24,0) (23,20) (27,20) (15,21) (18,8) (11,6) (5,21) (17,24) (5,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph753",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,20) (32,20) (32,25) (6,10) (0,3) (13,9) (11,20) (11,10) (2,1) (23,28) (10,13) (17,2) (18,25) (3,5) (5,23) (16,8) (30,24) (4,5) (1,14) (32,19) (31,15) (19,7) (10,27) (24,27) (22,28) (27,16) (14,15) (17,26) (23,29) (12,2) (23,21) (1,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph878",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,0) (33,4) (4,26) (24,27) (33,12) (21,4) (8,2) (32,23) (4,23) (32,0) (3,5) (27,2) (23,10) (26,29) (7,32) (18,22) (26,5) (18,15) (23,25) (20,9) (27,17) (13,28) (11,28) (2,33) (13,32) (6,29) (30,0) (16,24) (3,9) (14,6) (18,23) (28,19) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph818",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,19) (16,3) (20,7) (24,10) (12,9) (17,29) (29,1) (11,9) (17,24) (11,4) (19,13) (13,3) (18,32) (27,7) (14,21) (10,7) (25,6) (13,25) (27,15) (22,8) (31,21) (28,5) (29,25) (26,23) (9,0) (2,29) (33,7) (29,5) (13,26) (30,16) (11,32) (12,22) (22,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1094",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,0) (1,4) (22,14) (11,19) (3,22) (9,18) (24,15) (18,10) (18,12) (9,13) (8,9) (21,7) (6,15) (20,25) (2,17) (23,17) (1,0) (0,3) (8,11) (0,2) (5,2) (21,25) (15,8) (6,0) (20,16) (23,4) (18,14) (1,21) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph91",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,13) (12,18) (7,21) (25,21) (14,18) (23,4) (4,1) (24,15) (11,19) (10,18) (6,15) (0,6) (5,2) (3,22) (8,9) (20,25) (22,14) (1,21) (8,11) (11,2) (17,23) (18,9) (17,2) (15,8) (16,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph894",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (5,32) (20,27) (21,4) (33,16) (25,10) (14,22) (12,30) (11,19) (17,32) (30,28) (24,0) (19,6) (13,15) (16,25) (22,6) (8,23) (16,2) (6,31) (21,30) (20,13) (28,33) (26,9) (19,9) (4,29) (16,32) (8,18) (18,24) (1,26) (31,7) (8,6) (3,2) (27,22) (13,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph206",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,13) (3,17) (11,24) (21,1) (5,22) (15,14) (2,3) (6,20) (7,10) (19,5) (23,14) (25,3) (9,7) (23,12) (2,23) (6,10) (1,8) (26,17) (14,4) (16,25) (13,11) (0,4) (8,14) (24,18) (27,9) (22,12) (20,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1146",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,26) (1,24) (0,20) (1,0) (2,22) (18,9) (3,2) (7,25) (19,14) (23,4) (21,18) (13,12) (15,26) (7,19) (9,13) (14,8) (2,17) (4,11) (6,23) (11,16) (0,2) (9,5) (0,14) (8,6) (0,3) (22,15) (24,0) (12,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1744",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,17) (22,18) (2,16) (3,20) (24,29) (0,3) (25,0) (23,15) (16,31) (8,15) (31,1) (5,7) (12,27) (10,12) (7,19) (21,11) (0,17) (14,13) (11,24) (32,28) (5,32) (4,12) (21,20) (4,5) (11,26) (1,0) (30,13) (14,12) (0,2) (9,32) (18,30) (30,16) (7,20) (15,9) (12,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1401",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,24) (10,17) (0,21) (26,16) (25,29) (29,9) (27,13) (2,19) (11,7) (15,25) (8,10) (1,0) (14,23) (10,16) (3,0) (25,19) (18,14) (13,22) (28,17) (18,13) (17,21) (11,29) (1,4) (6,5) (25,3) (0,2) (12,27) (25,17) (26,14) (20,27) (5,2) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph96",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,12) (21,18) (10,23) (8,9) (13,20) (19,1) (25,12) (9,17) (23,16) (6,22) (23,24) (5,21) (19,6) (19,8) (25,14) (3,2) (18,1) (4,2) (1,0) (2,11) (15,21) (11,16) (25,11) (7,5) (5,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1814",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (16,30) (20,3) (2,16) (20,21) (13,14) (33,12) (6,12) (22,18) (5,4) (29,24) (7,19) (13,30) (9,32) (16,31) (27,12) (10,12) (18,30) (24,11) (8,15) (15,9) (11,26) (0,25) (1,0) (23,15) (4,32) (31,1) (32,28) (20,7) (2,0) (5,7) (1,17) (14,12) (5,12) (17,0) (21,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph19",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,14) (16,9) (14,23) (3,8) (17,0) (13,20) (13,11) (11,25) (8,19) (9,5) (13,9) (3,4) (8,17) (25,24) (0,7) (18,19) (23,0) (0,21) (1,17) (15,12) (2,5) (15,11) (6,13) (21,10) (13,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1672",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,9) (27,23) (15,10) (29,5) (0,1) (11,28) (11,21) (8,5) (30,20) (6,11) (18,5) (5,30) (29,9) (22,12) (2,25) (12,26) (7,14) (23,24) (21,5) (13,26) (12,4) (31,19) (14,8) (31,0) (16,24) (0,17) (24,3) (2,17) (24,13) (25,20) (15,16) (25,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph124",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (6,23) (4,11) (26,10) (0,14) (21,18) (22,15) (23,4) (7,25) (9,18) (2,22) (20,0) (9,5) (17,2) (7,19) (11,16) (6,8) (26,15) (16,12) (2,3) (9,13) (13,12) (0,3) (14,19) (1,24) (14,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1978",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,33) (2,9) (23,31) (13,6) (13,3) (14,25) (29,32) (28,22) (34,24) (0,4) (19,5) (29,18) (18,9) (3,0) (34,16) (12,17) (27,21) (19,30) (27,22) (12,9) (27,8) (6,12) (11,26) (20,24) (1,0) (15,11) (21,26) (3,23) (11,30) (25,0) (6,4) (23,11) (9,33) (10,2) (15,0) (2,0) (12,1) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1228",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,19) (26,5) (18,12) (18,6) (7,17) (1,10) (22,25) (8,25) (17,9) (3,23) (15,5) (13,0) (27,1) (0,1) (25,11) (10,20) (13,8) (17,21) (0,2) (18,21) (26,25) (20,21) (18,3) (15,16) (18,2) (16,4) (2,26) (14,25) (24,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph843",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,26) (1,17) (25,5) (25,13) (31,5) (4,24) (31,28) (7,24) (6,33) (3,23) (2,5) (0,14) (31,14) (9,8) (30,26) (22,31) (15,8) (20,1) (16,6) (10,12) (33,17) (1,14) (29,12) (23,29) (11,2) (30,24) (8,18) (13,19) (25,12) (15,32) (27,24) (29,21) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1096",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,17) (17,21) (23,3) (2,18) (5,2) (5,15) (25,11) (18,3) (8,13) (24,19) (12,18) (18,21) (16,24) (0,13) (4,16) (25,1) (20,21) (18,6) (1,10) (8,25) (9,17) (25,22) (15,16) (14,25) (10,20) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph697",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,9) (21,13) (17,11) (31,21) (7,17) (16,20) (28,7) (15,24) (11,14) (0,26) (9,12) (23,6) (29,5) (4,7) (19,2) (26,21) (1,18) (20,25) (26,19) (19,4) (3,25) (13,27) (30,5) (16,23) (1,15) (8,24) (8,12) (22,26) (26,9) (8,3) (18,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph12",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,16) (15,1) (4,22) (2,6) (19,4) (11,20) (18,21) (23,13) (14,22) (12,8) (5,7) (0,6) (5,16) (12,24) (0,17) (8,23) (1,0) (1,25) (11,25) (22,11) (10,14) (10,3) (11,8) (7,21) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1364",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,25) (10,23) (2,0) (0,3) (28,2) (28,22) (10,26) (5,27) (16,4) (17,27) (3,9) (1,0) (2,7) (14,11) (26,7) (7,9) (17,21) (14,12) (22,19) (20,24) (18,16) (17,14) (15,19) (13,0) (9,1) (6,8) (13,28) (20,6) (4,0) (14,16) (14,8) (15,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph286",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (8,6) (15,9) (15,13) (11,10) (10,3) (4,14) (7,6) (23,6) (15,18) (27,5) (5,25) (14,9) (21,16) (19,5) (25,24) (24,21) (27,26) (7,12) (2,21) (22,8) (15,20) (22,3) (1,3) (17,20) (14,8) (10,16) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1077",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,15) (3,10) (2,21) (0,2) (11,10) (8,14) (20,6) (12,7) (5,0) (0,3) (25,23) (15,18) (22,3) (14,4) (14,9) (20,17) (24,25) (6,7) (15,13) (1,0) (24,21) (1,3) (5,19) (8,6) (10,16) (8,22) (9,15) (21,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph348",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,17) (19,22) (5,4) (26,21) (15,3) (16,14) (0,17) (27,17) (13,5) (9,12) (20,15) (7,20) (6,7) (16,24) (8,17) (27,28) (18,6) (10,1) (13,23) (25,9) (17,11) (24,22) (25,4) (4,2) (27,25) (10,22) (21,3) (24,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph440",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (6,0) (29,26) (9,14) (4,24) (28,27) (27,3) (22,8) (12,27) (2,12) (7,26) (16,20) (3,18) (9,1) (18,25) (24,20) (10,26) (13,24) (26,23) (18,9) (1,15) (15,17) (18,21) (23,21) (27,19) (13,3) (6,29) (29,5) (8,1) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1017",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,8) (21,5) (18,9) (2,22) (21,2) (7,20) (13,0) (6,9) (0,3) (18,15) (4,11) (0,2) (17,25) (1,0) (12,1) (7,1) (1,10) (9,3) (24,25) (25,19) (16,8) (4,12) (10,14) (15,14) (23,0) (25,20) (5,4) (13,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph309",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,13) (10,11) (6,3) (4,2) (16,7) (26,22) (19,11) (15,20) (27,9) (4,1) (17,7) (14,5) (13,15) (9,5) (25,22) (6,0) (15,26) (22,11) (14,8) (23,15) (21,4) (11,2) (3,23) (24,0) (28,19) (22,18) (7,23) (19,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1285",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,2) (12,27) (2,0) (19,22) (12,5) (21,4) (23,11) (26,25) (23,16) (21,8) (7,6) (26,14) (25,11) (0,4) (1,0) (8,7) (3,0) (27,6) (21,3) (18,14) (14,17) (14,10) (6,15) (25,13) (25,6) (14,20) (26,19) (18,1) (15,24) (9,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph123",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,10) (18,22) (15,21) (25,6) (14,12) (14,10) (26,2) (2,22) (25,17) (7,6) (3,5) (16,0) (15,11) (10,8) (1,15) (22,16) (10,9) (25,5) (10,20) (0,20) (24,12) (2,11) (13,9) (4,17) (23,11) (0,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1280",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,0) (3,18) (22,18) (0,3) (1,15) (3,13) (0,10) (21,18) (26,27) (2,0) (9,1) (8,1) (24,4) (24,27) (13,20) (9,11) (27,6) (7,26) (15,14) (21,23) (12,20) (1,0) (2,12) (8,19) (3,25) (23,26) (17,24) (27,16) (26,5) (9,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1284",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,0) (11,5) (13,20) (14,24) (14,18) (6,21) (0,3) (23,4) (1,0) (23,2) (4,19) (0,6) (5,12) (24,12) (27,7) (6,19) (19,9) (25,4) (2,0) (26,5) (20,17) (4,16) (7,15) (7,13) (3,4) (26,6) (22,10) (8,17) (22,6) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1426",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,9) (27,12) (14,7) (19,26) (25,23) (10,15) (20,28) (24,0) (27,0) (16,29) (19,11) (7,16) (0,3) (3,20) (13,20) (8,0) (28,29) (0,2) (16,5) (12,3) (6,19) (22,12) (0,1) (13,9) (1,11) (17,10) (2,1) (12,11) (28,21) (5,23) (18,26) (18,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1930",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,26) (28,19) (0,1) (24,16) (23,10) (17,27) (33,12) (25,27) (24,18) (29,6) (13,32) (26,30) (34,22) (0,31) (33,2) (23,4) (9,20) (3,0) (2,28) (21,4) (0,2) (5,3) (32,0) (3,9) (5,1) (26,5) (32,7) (34,4) (13,29) (27,23) (14,6) (11,28) (2,8) (23,32) (33,0) (15,18) (18,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1587",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,11) (28,30) (19,9) (13,23) (17,2) (12,1) (28,25) (16,21) (1,0) (19,26) (0,3) (6,15) (2,14) (7,5) (23,19) (13,29) (18,6) (20,8) (23,8) (5,10) (2,30) (3,6) (12,24) (4,7) (12,16) (6,25) (12,0) (27,15) (22,21) (24,4) (0,2) (17,22) (18,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1323",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,16) (12,22) (4,2) (16,19) (18,26) (0,13) (19,15) (1,12) (10,25) (17,3) (7,0) (14,23) (20,12) (5,26) (26,27) (14,0) (20,17) (4,20) (28,16) (8,1) (7,25) (0,1) (0,2) (6,8) (5,2) (19,9) (26,19) (9,11) (21,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1304",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,0) (16,21) (8,2) (28,4) (11,16) (7,19) (3,10) (1,19) (6,2) (2,0) (1,0) (22,27) (13,4) (1,23) (6,19) (17,24) (22,16) (16,5) (0,26) (24,14) (26,11) (15,26) (4,24) (9,25) (16,6) (18,6) (8,20) (0,10) (14,26) (8,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph217",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,15) (11,15) (5,24) (24,4) (8,17) (26,21) (19,25) (12,2) (16,4) (11,18) (26,9) (12,25) (12,20) (18,6) (8,25) (4,9) (10,1) (8,1) (14,15) (13,7) (27,0) (13,16) (24,3) (6,16) (17,27) (22,9) (3,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph592",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,6) (22,29) (9,13) (16,17) (15,20) (30,29) (12,0) (11,8) (4,15) (23,9) (25,9) (3,14) (24,25) (1,7) (5,24) (5,26) (3,8) (4,2) (17,12) (30,6) (17,11) (2,21) (0,2) (3,26) (10,7) (23,18) (28,24) (27,1) (12,19) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph923",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,13) (29,10) (19,3) (32,8) (15,22) (20,6) (12,9) (7,27) (31,10) (9,19) (1,29) (17,16) (6,18) (17,26) (25,17) (30,12) (14,30) (21,31) (12,8) (23,22) (20,5) (29,11) (28,29) (5,16) (2,32) (33,31) (22,31) (27,24) (0,28) (4,3) (24,34) (4,34) (19,1) (26,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1414",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,4) (18,6) (22,21) (0,12) (2,14) (13,27) (19,23) (24,4) (13,23) (16,21) (5,10) (15,6) (7,5) (17,2) (15,26) (18,19) (17,22) (25,6) (6,3) (12,24) (0,1) (23,8) (2,19) (16,12) (12,1) (28,29) (25,28) (11,7) (8,20) (9,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph63",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (12,20) (2,14) (2,17) (16,12) (15,6) (23,13) (7,5) (17,22) (19,9) (21,16) (8,18) (23,8) (0,12) (4,7) (15,24) (3,6) (5,10) (25,19) (22,21) (7,11) (2,19) (24,4) (1,12) (6,13) (19,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph866",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,9) (30,5) (24,16) (5,19) (17,0) (27,12) (23,28) (4,12) (15,10) (16,15) (5,32) (5,21) (20,25) (33,31) (14,8) (22,31) (24,23) (11,21) (6,11) (33,0) (13,24) (14,7) (18,33) (30,20) (26,13) (12,26) (1,25) (13,9) (25,2) (24,3) (5,8) (2,17) (29,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1517",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,18) (14,0) (17,2) (15,16) (9,14) (27,1) (4,2) (16,21) (22,30) (15,20) (14,12) (0,1) (25,19) (9,4) (29,5) (24,18) (25,17) (5,3) (22,28) (3,14) (27,8) (24,11) (23,27) (25,26) (19,20) (6,5) (16,27) (13,14) (7,17) (25,28) (0,2) (10,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1250",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (2,10) (27,18) (19,12) (15,22) (10,13) (19,14) (2,20) (18,2) (21,22) (22,9) (21,10) (9,6) (11,17) (5,14) (5,26) (27,4) (0,1) (4,23) (27,7) (11,27) (19,0) (2,1) (16,8) (24,3) (4,8) (0,3) (2,0) (0,4) (6,25) (24,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph308",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,17) (1,23) (26,8) (10,2) (11,28) (25,22) (18,22) (11,20) (13,9) (24,5) (15,18) (24,18) (4,6) (12,10) (23,25) (3,24) (8,13) (8,20) (14,4) (24,16) (17,0) (25,27) (19,16) (21,27) (10,27) (7,23) (3,11) (4,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1603",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,17) (13,31) (30,0) (3,0) (13,22) (7,26) (19,21) (24,8) (10,14) (25,24) (11,24) (20,16) (1,9) (12,13) (13,4) (8,3) (24,9) (13,16) (11,15) (19,5) (0,4) (6,12) (0,2) (6,14) (29,6) (1,0) (4,18) (26,1) (30,28) (11,28) (4,8) (23,3) (21,1) (15,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1913",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,21) (17,10) (23,28) (20,29) (9,32) (4,0) (26,28) (8,25) (19,22) (32,5) (31,5) (10,16) (26,34) (15,22) (20,22) (14,11) (12,6) (30,31) (5,27) (4,31) (33,23) (19,12) (31,11) (18,13) (0,3) (30,7) (8,7) (15,0) (3,9) (1,34) (1,19) (16,18) (27,2) (0,11) (2,10) (1,0) (0,2) (24,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph990",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,16) (31,2) (6,0) (12,34) (7,33) (9,20) (9,2) (18,32) (27,2) (0,15) (16,33) (32,28) (14,21) (29,2) (25,26) (25,21) (24,29) (10,20) (18,34) (13,29) (17,31) (6,33) (11,12) (5,0) (33,31) (34,22) (3,2) (31,4) (18,1) (12,15) (19,23) (9,30) (8,14) (30,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1223",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,0) (12,20) (14,15) (22,18) (21,18) (10,0) (7,26) (2,12) (8,1) (26,27) (3,13) (3,25) (23,21) (23,26) (1,0) (16,27) (5,26) (27,6) (15,1) (8,19) (24,27) (9,11) (18,9) (17,24) (4,24) (9,1) (18,3) (20,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1708",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,0) (21,29) (7,29) (28,12) (3,9) (16,21) (14,11) (31,26) (4,21) (0,11) (12,14) (19,8) (2,12) (27,8) (23,7) (11,25) (8,18) (20,27) (5,11) (0,1) (28,30) (6,0) (28,15) (10,19) (8,24) (7,10) (29,17) (26,20) (14,22) (21,3) (15,9) (25,1) (13,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph379",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,10) (8,23) (0,24) (14,21) (18,16) (3,0) (20,5) (21,5) (11,17) (5,4) (15,26) (18,1) (5,27) (14,12) (19,5) (2,6) (16,0) (3,25) (9,13) (15,27) (8,20) (16,15) (2,26) (22,0) (9,28) (7,28) (11,5) (28,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1894",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (9,19) (24,2) (31,32) (0,1) (28,24) (26,0) (1,14) (18,15) (22,30) (16,20) (9,13) (2,15) (2,21) (18,12) (4,33) (32,3) (2,0) (17,15) (26,10) (14,16) (7,19) (25,21) (11,9) (5,11) (9,30) (4,0) (9,1) (29,23) (0,3) (8,19) (6,19) (8,10) (17,4) (5,27) (6,3) (18,14) (29,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1372",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (23,12) (27,17) (3,17) (10,6) (16,13) (0,1) (6,20) (1,21) (18,24) (26,28) (0,4) (14,15) (23,2) (14,4) (23,14) (7,9) (3,25) (26,9) (11,24) (14,8) (12,22) (11,13) (1,8) (16,25) (21,20) (5,19) (10,7) (5,22) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph414",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,18) (17,15) (29,20) (20,12) (15,23) (29,0) (5,17) (15,12) (11,19) (29,10) (15,22) (8,17) (16,18) (17,27) (19,2) (4,9) (6,22) (8,24) (18,2) (28,26) (11,4) (21,26) (7,25) (20,14) (7,6) (13,15) (7,1) (17,26) (0,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1839",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,27) (8,16) (33,0) (12,8) (14,17) (9,25) (26,6) (3,8) (33,31) (26,19) (13,9) (2,0) (3,0) (1,0) (7,14) (4,15) (28,14) (32,17) (28,8) (21,13) (24,12) (12,25) (20,26) (0,12) (10,23) (7,2) (8,20) (26,1) (13,22) (29,18) (10,8) (11,32) (4,6) (11,5) (30,11) (15,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph232",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,27) (24,13) (23,13) (17,8) (9,13) (0,12) (16,21) (17,1) (20,9) (9,6) (3,26) (15,11) (7,13) (13,11) (14,26) (25,0) (5,2) (23,0) (22,8) (19,21) (26,19) (0,17) (5,8) (18,15) (14,11) (27,11) (4,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph76",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,0) (11,16) (4,9) (25,17) (24,22) (14,9) (4,2) (6,5) (18,12) (24,7) (16,15) (19,20) (15,20) (19,25) (17,2) (21,16) (13,6) (22,25) (8,14) (23,5) (3,14) (14,10) (18,25) (3,5) (1,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1706",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,7) (1,5) (29,19) (0,4) (22,16) (10,31) (4,7) (13,17) (14,20) (28,15) (28,16) (15,3) (1,0) (9,10) (32,24) (2,0) (3,0) (13,24) (27,25) (30,17) (23,16) (7,21) (22,20) (14,29) (2,6) (25,26) (8,16) (19,18) (0,10) (1,21) (12,4) (9,23) (6,17) (18,11) (5,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph964",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,33) (14,25) (11,30) (30,19) (0,15) (18,29) (34,16) (24,34) (27,21) (8,27) (12,6) (16,7) (11,23) (20,24) (31,23) (6,13) (17,12) (21,26) (4,6) (15,11) (2,10) (0,25) (27,22) (33,9) (18,9) (9,12) (13,3) (26,11) (2,9) (22,28) (1,12) (23,3) (19,5) (32,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1079",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,17) (4,3) (15,25) (15,7) (24,2) (9,6) (3,15) (23,18) (19,5) (21,20) (25,12) (1,22) (6,24) (13,1) (1,0) (3,18) (8,5) (0,4) (9,11) (14,5) (15,13) (21,8) (5,24) (16,10) (17,9) (2,0) (25,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1808",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,25) (27,7) (19,14) (13,3) (5,29) (7,33) (24,17) (4,11) (19,13) (22,12) (32,18) (2,29) (28,5) (31,21) (7,20) (24,10) (16,3) (30,16) (29,1) (11,9) (14,21) (26,13) (15,27) (8,22) (0,1) (10,7) (26,23) (9,12) (9,0) (23,22) (17,29) (25,6) (11,32) (29,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1430",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (24,17) (2,8) (7,27) (13,14) (0,4) (18,0) (21,12) (1,0) (0,2) (26,24) (7,5) (29,4) (23,17) (12,7) (0,11) (27,10) (1,19) (16,5) (20,17) (28,19) (6,17) (11,22) (16,18) (25,12) (28,8) (12,1) (11,15) (29,26) (22,9) (3,12) (11,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph771",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,23) (16,0) (32,21) (9,31) (21,0) (16,26) (7,27) (19,13) (1,11) (22,18) (10,15) (5,15) (12,25) (2,7) (20,11) (19,16) (11,15) (11,14) (21,4) (6,12) (31,8) (30,12) (31,13) (12,15) (20,7) (23,32) (31,12) (28,10) (18,29) (17,30) (24,16) (3,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph487",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,8) (8,20) (4,14) (2,8) (0,17) (3,21) (27,22) (0,12) (22,26) (19,4) (7,17) (7,28) (16,6) (19,21) (10,5) (21,0) (16,4) (12,18) (25,20) (14,11) (29,10) (15,24) (23,11) (27,19) (21,9) (5,11) (25,14) (13,11) (15,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1631",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,25) (23,27) (8,2) (2,0) (11,28) (23,4) (9,3) (0,30) (28,2) (1,14) (0,29) (4,14) (28,19) (26,5) (0,3) (18,15) (23,18) (24,16) (9,21) (12,6) (22,4) (24,18) (2,13) (23,0) (26,13) (27,17) (5,7) (5,3) (20,31) (29,6) (4,26) (20,1) (10,23) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1777",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,8) (27,20) (0,20) (0,25) (6,0) (9,16) (14,26) (30,16) (28,30) (15,28) (12,21) (13,25) (24,11) (1,19) (23,22) (15,14) (2,23) (22,3) (4,5) (22,21) (12,15) (6,1) (10,32) (29,7) (4,27) (32,27) (2,17) (15,32) (29,22) (1,0) (2,31) (18,26) (0,2) (24,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph247",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,14) (8,13) (18,2) (13,11) (5,20) (23,8) (18,9) (15,2) (12,16) (24,25) (0,26) (3,4) (8,1) (16,22) (27,24) (19,18) (12,15) (16,7) (15,10) (17,27) (6,14) (6,16) (17,11) (0,13) (5,14) (0,3) (21,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph103",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,5) (6,10) (20,17) (6,13) (10,11) (8,23) (5,25) (19,7) (14,3) (15,9) (4,17) (20,21) (4,7) (24,15) (7,12) (17,18) (6,26) (0,26) (8,0) (25,1) (22,19) (16,0) (21,16) (25,26) (9,3) (8,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph270",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,13) (15,16) (22,8) (1,5) (16,9) (9,10) (0,9) (18,4) (12,11) (21,2) (19,4) (16,7) (21,3) (24,3) (25,8) (10,24) (11,16) (6,17) (12,6) (25,1) (23,13) (18,20) (27,0) (3,26) (8,26) (3,14) (8,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph455",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,18) (11,22) (19,28) (16,20) (4,1) (15,6) (24,25) (28,15) (20,29) (18,10) (21,7) (8,9) (3,22) (21,1) (18,28) (26,27) (23,4) (2,5) (9,13) (9,26) (12,18) (17,2) (17,23) (14,25) (11,2) (15,8) (21,20) (6,0) (11,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1699",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,17) (26,25) (17,12) (11,29) (0,20) (1,21) (1,26) (14,29) (12,8) (1,27) (4,18) (28,2) (6,24) (5,31) (1,9) (3,22) (23,31) (19,10) (16,24) (8,19) (0,4) (23,13) (2,0) (0,14) (18,22) (3,13) (27,22) (30,23) (1,0) (23,2) (27,15) (5,7) (5,6) (3,0) (13,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1445",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,2) (9,26) (21,7) (15,8) (16,20) (11,8) (0,3) (13,9) (25,14) (18,10) (17,23) (11,2) (2,5) (12,18) (3,22) (2,17) (0,1) (21,1) (11,22) (14,18) (15,28) (29,20) (1,4) (0,6) (8,9) (28,19) (21,20) (24,25) (6,15) (18,28) (23,4) (27,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph319",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,27) (0,4) (25,12) (22,11) (2,8) (22,9) (12,21) (20,17) (28,4) (11,13) (11,0) (18,16) (15,11) (5,16) (6,17) (0,18) (28,8) (7,26) (12,3) (24,26) (12,1) (23,17) (7,12) (1,19) (27,19) (13,14) (17,24) (7,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1960",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,20) (18,29) (23,17) (3,0) (14,29) (32,14) (1,11) (15,7) (19,28) (29,34) (13,22) (5,29) (15,10) (21,22) (22,20) (8,2) (26,33) (9,23) (25,17) (16,24) (3,1) (15,12) (13,27) (31,26) (10,2) (4,13) (25,14) (0,6) (30,26) (1,0) (22,16) (32,19) (3,9) (21,7) (0,33) (5,31) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1867",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,1) (21,11) (19,24) (24,23) (3,10) (13,23) (30,22) (25,4) (24,25) (15,14) (33,2) (5,26) (27,31) (28,19) (8,29) (24,22) (18,13) (1,0) (5,0) (31,17) (24,11) (28,7) (29,9) (5,28) (16,13) (29,6) (21,32) (16,10) (15,12) (16,2) (12,23) (27,11) (5,29) (13,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1788",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (26,10) (15,9) (7,28) (2,4) (1,0) (22,10) (16,6) (1,27) (13,0) (8,23) (6,31) (7,24) (19,32) (29,31) (25,29) (13,20) (20,30) (19,3) (23,1) (18,8) (18,14) (3,0) (8,24) (28,12) (32,26) (21,4) (29,11) (19,30) (17,11) (29,13) (15,16) (27,5) (0,2) (23,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph621",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,5) (8,16) (8,7) (10,27) (24,2) (21,0) (14,26) (25,10) (0,11) (24,6) (15,3) (13,18) (12,17) (23,9) (24,4) (31,17) (23,21) (29,1) (5,26) (29,20) (15,10) (6,18) (2,21) (30,10) (3,7) (5,22) (29,28) (11,19) (14,13) (27,28) (4,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph37",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,6) (8,15) (17,2) (9,5) (18,10) (18,23) (6,12) (7,13) (0,4) (2,19) (9,15) (23,21) (22,6) (14,3) (25,15) (25,17) (14,7) (14,19) (12,20) (12,11) (4,17) (16,10) (1,15) (23,17) (24,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph769",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,8) (2,12) (0,32) (13,0) (20,26) (21,16) (12,14) (0,11) (15,28) (8,18) (15,9) (29,17) (10,19) (27,8) (14,11) (4,21) (3,21) (10,7) (23,7) (6,0) (29,21) (9,3) (11,5) (29,7) (22,14) (11,25) (8,19) (20,27) (30,28) (1,25) (26,31) (12,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1388",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,19) (5,4) (24,22) (9,7) (15,12) (11,23) (14,20) (5,18) (4,28) (26,24) (10,26) (3,0) (17,13) (2,0) (7,11) (16,12) (17,0) (16,1) (10,9) (2,26) (27,23) (19,25) (21,14) (0,28) (4,21) (8,17) (15,26) (21,9) (6,10) (1,0) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1121",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,0) (15,22) (21,3) (0,1) (4,7) (18,11) (4,14) (24,17) (23,0) (9,21) (5,22) (19,14) (9,1) (13,12) (18,25) (12,26) (1,2) (22,10) (19,17) (11,8) (6,24) (20,25) (13,24) (14,3) (19,15) (11,19) (13,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1396",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,7) (11,26) (18,7) (27,22) (13,15) (23,0) (2,0) (3,12) (14,1) (3,25) (19,18) (4,23) (27,24) (1,0) (24,20) (19,16) (6,26) (3,0) (17,20) (16,9) (21,23) (10,21) (14,10) (14,17) (28,3) (5,11) (17,5) (8,15) (2,22) (25,24) (23,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1005",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (23,4) (17,12) (11,5) (24,25) (11,8) (1,16) (20,2) (18,21) (0,19) (7,15) (4,16) (19,11) (14,0) (24,4) (8,3) (1,0) (18,16) (6,18) (10,9) (0,7) (13,9) (12,11) (10,3) (22,3) (13,2) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1124",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,16) (3,4) (7,12) (23,19) (8,14) (9,14) (21,17) (0,2) (22,6) (24,12) (25,13) (12,20) (3,15) (1,0) (9,1) (21,22) (22,5) (14,10) (26,4) (4,11) (2,16) (0,3) (18,21) (21,13) (20,2) (0,4) (6,19) (25,7) (26,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1182",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (24,5) (11,17) (23,1) (12,17) (3,25) (26,3) (20,2) (3,13) (9,25) (6,7) (14,23) (5,26) (18,12) (2,4) (1,0) (15,19) (11,8) (24,8) (9,10) (7,16) (17,16) (1,7) (15,4) (12,0) (24,22) (9,21) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph139",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,0) (5,8) (23,26) (7,15) (8,4) (0,3) (20,1) (25,21) (2,4) (23,9) (3,9) (8,25) (2,12) (23,25) (13,6) (1,19) (14,10) (19,2) (9,13) (11,8) (15,0) (3,22) (17,15) (20,24) (9,18) (16,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1237",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,13) (12,19) (21,10) (0,19) (19,14) (11,27) (3,0) (13,10) (9,6) (11,17) (0,7) (22,9) (25,6) (15,22) (5,26) (20,2) (2,10) (1,2) (2,18) (16,8) (27,7) (4,23) (2,0) (18,27) (5,14) (22,21) (27,4) (1,0) (8,4) (24,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph226",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,10) (13,19) (24,9) (16,24) (17,14) (21,25) (27,0) (2,8) (14,15) (24,26) (0,15) (1,4) (15,11) (24,0) (19,24) (12,20) (3,6) (20,18) (12,13) (22,6) (12,25) (26,23) (15,3) (7,25) (5,27) (4,18) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph174",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,10) (20,2) (5,23) (4,9) (0,26) (14,21) (24,9) (25,15) (16,19) (26,21) (17,9) (22,11) (18,23) (15,12) (14,6) (1,7) (0,13) (25,17) (10,21) (0,7) (24,5) (12,22) (2,3) (0,19) (15,20) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph548",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,15) (0,2) (1,27) (16,17) (1,7) (7,16) (9,23) (30,29) (11,17) (3,26) (18,23) (28,24) (25,9) (19,12) (3,8) (30,6) (24,25) (13,9) (10,7) (11,8) (5,24) (21,2) (6,8) (12,0) (5,26) (3,14) (4,2) (15,20) (29,22) (12,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1732",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,17) (23,15) (15,9) (6,12) (12,27) (18,22) (28,32) (26,11) (8,15) (0,1) (2,0) (18,30) (11,24) (29,24) (0,17) (16,30) (25,0) (2,16) (4,5) (30,13) (14,13) (5,32) (7,20) (4,12) (31,1) (21,20) (10,12) (11,21) (14,12) (16,31) (19,7) (32,9) (3,20) (7,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1090",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,18) (25,11) (15,7) (2,17) (5,12) (17,6) (0,3) (23,6) (4,0) (21,10) (0,1) (24,2) (0,13) (5,22) (3,9) (23,9) (8,1) (4,21) (8,21) (21,16) (19,7) (25,21) (4,13) (7,20) (0,9) (20,23) (0,2) (20,14) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph656",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,26) (17,18) (12,3) (6,17) (12,28) (20,19) (29,7) (18,10) (12,7) (1,6) (9,11) (7,2) (14,16) (5,25) (6,4) (24,4) (31,25) (26,30) (16,20) (2,0) (29,24) (22,12) (9,16) (13,6) (27,25) (1,26) (21,20) (6,27) (23,4) (19,1) (22,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph613",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,17) (18,9) (8,21) (0,6) (5,20) (14,3) (1,23) (20,15) (21,26) (21,29) (22,0) (1,3) (2,21) (4,10) (27,12) (31,30) (3,28) (23,25) (5,10) (15,1) (16,13) (27,31) (0,24) (7,8) (6,31) (30,4) (10,21) (23,19) (16,17) (9,11) (6,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1920",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,30) (16,9) (22,1) (4,3) (6,10) (10,27) (7,24) (11,25) (2,7) (22,15) (13,30) (5,33) (7,8) (23,22) (20,2) (26,14) (6,5) (10,3) (13,25) (28,18) (4,30) (19,10) (4,7) (9,11) (25,23) (21,13) (5,12) (18,34) (32,4) (31,0) (1,0) (17,7) (5,18) (29,18) (31,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph345",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (28,12) (8,7) (16,25) (25,6) (3,21) (14,10) (19,23) (21,4) (24,11) (18,14) (18,1) (27,13) (15,26) (5,2) (25,11) (5,9) (14,21) (12,6) (8,22) (6,7) (20,14) (2,0) (14,26) (27,25) (19,26) (6,15) (5,12) (23,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph686",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,21) (29,27) (28,22) (24,11) (13,17) (10,15) (8,29) (12,14) (19,24) (6,28) (19,26) (5,25) (16,13) (3,25) (21,11) (28,5) (11,1) (7,29) (29,4) (24,22) (11,27) (20,5) (12,23) (13,31) (10,2) (18,24) (9,16) (24,23) (13,23) (0,5) (31,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph369",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (28,19) (21,1) (20,16) (3,22) (15,27) (23,17) (2,5) (17,2) (18,12) (8,9) (0,6) (4,1) (28,18) (18,10) (26,9) (2,11) (18,14) (8,15) (25,22) (7,21) (23,4) (24,14) (11,8) (26,25) (15,6) (21,28) (20,11) (13,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1789",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (26,0) (24,5) (2,14) (31,20) (32,22) (21,6) (0,1) (15,22) (9,20) (28,20) (26,19) (20,23) (7,32) (13,6) (20,1) (2,1) (10,1) (25,11) (17,25) (2,0) (30,0) (10,3) (27,30) (17,8) (10,18) (13,12) (3,7) (32,8) (22,21) (28,29) (5,16) (23,4) (15,30) (21,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph881",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,31) (3,32) (8,19) (15,18) (1,9) (26,0) (14,18) (2,24) (27,5) (11,5) (30,22) (29,0) (9,30) (29,23) (4,33) (20,16) (8,10) (11,9) (2,21) (16,14) (17,4) (17,15) (3,6) (14,1) (28,24) (6,19) (13,9) (25,21) (7,19) (18,12) (15,2) (10,26) (19,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1627",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,0) (8,5) (17,4) (23,19) (6,3) (13,18) (22,25) (12,15) (31,0) (24,26) (0,2) (11,31) (27,15) (2,21) (7,31) (14,17) (21,17) (15,25) (27,16) (10,20) (31,23) (4,26) (29,13) (18,11) (18,1) (0,10) (7,28) (20,30) (24,22) (5,0) (3,0) (10,25) (9,11) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph556",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,11) (15,17) (27,4) (13,27) (1,13) (15,16) (26,22) (3,18) (0,18) (7,2) (30,4) (6,14) (2,10) (16,26) (5,1) (25,20) (11,1) (29,23) (10,15) (21,15) (28,30) (12,13) (9,1) (24,8) (8,20) (6,0) (7,30) (5,25) (19,18) (14,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1483",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,13) (0,1) (27,13) (27,12) (11,7) (25,3) (9,29) (29,11) (10,8) (25,19) (1,3) (0,21) (19,2) (14,18) (23,14) (17,25) (25,29) (5,2) (2,0) (10,17) (13,22) (5,6) (20,27) (26,14) (24,26) (28,17) (4,1) (26,16) (21,17) (16,10) (15,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1019",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,4) (22,17) (2,15) (22,19) (2,24) (25,22) (0,1) (0,11) (8,9) (0,3) (10,14) (1,4) (10,21) (23,4) (3,23) (8,0) (17,20) (16,15) (12,8) (12,24) (18,20) (16,19) (7,3) (22,10) (11,3) (13,24) (17,6) (6,5) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1617",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,17) (15,4) (18,11) (10,8) (31,17) (2,7) (30,10) (8,13) (30,26) (27,10) (26,16) (0,2) (4,10) (12,2) (24,22) (28,14) (5,3) (3,30) (0,15) (28,19) (26,9) (31,24) (28,23) (2,21) (0,20) (1,0) (11,22) (26,7) (31,29) (24,2) (0,25) (23,6) (14,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1838",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,24) (29,22) (4,25) (6,17) (0,33) (3,13) (10,33) (3,25) (29,5) (32,8) (10,26) (0,1) (1,15) (1,25) (19,8) (0,2) (0,20) (11,13) (7,31) (17,7) (9,1) (1,23) (16,12) (18,5) (4,22) (25,28) (3,0) (15,17) (30,27) (4,24) (33,19) (31,19) (21,15) (2,18) (6,27) (8,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph939",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (27,16) (1,14) (15,33) (19,7) (14,15) (23,30) (17,28) (23,5) (16,8) (0,3) (27,33) (13,10) (28,25) (21,23) (3,5) (9,13) (1,11) (20,11) (10,6) (20,34) (32,26) (22,34) (12,2) (24,27) (20,29) (2,17) (18,25) (10,32) (11,10) (31,24) (32,19) (29,23) (1,2) (5,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1068",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,12) (23,19) (20,21) (13,3) (17,6) (18,24) (0,14) (24,4) (3,12) (16,17) (0,1) (7,10) (9,20) (23,8) (0,10) (11,24) (16,3) (18,0) (2,15) (24,25) (1,25) (22,2) (23,16) (9,23) (14,13) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1207",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,0) (13,20) (2,0) (27,26) (22,1) (13,5) (20,10) (6,12) (26,3) (14,21) (0,27) (6,3) (8,2) (24,18) (23,2) (8,11) (8,4) (0,25) (10,17) (9,10) (10,24) (11,10) (21,0) (4,16) (15,12) (16,25) (11,7) (1,19) (5,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1541",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,22) (29,2) (13,0) (14,15) (12,4) (7,20) (27,5) (24,29) (0,28) (3,9) (1,12) (18,15) (11,4) (28,14) (10,19) (13,30) (0,1) (21,2) (25,23) (25,20) (27,26) (7,1) (8,16) (10,28) (9,18) (5,4) (2,0) (7,8) (6,9) (25,17) (21,27) (28,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1926",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,10) (5,1) (23,16) (31,9) (17,32) (29,19) (18,12) (10,0) (1,0) (4,0) (33,3) (33,10) (14,30) (16,22) (2,0) (16,29) (28,18) (17,13) (6,2) (17,8) (4,7) (24,34) (25,27) (21,1) (5,17) (20,22) (20,14) (7,25) (23,33) (21,7) (26,19) (15,6) (11,16) (4,15) (13,24) (25,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph980",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (15,20) (34,21) (25,4) (21,2) (26,28) (31,7) (10,18) (27,32) (33,31) (13,16) (23,0) (18,11) (1,23) (0,15) (22,0) (2,14) (4,9) (34,5) (29,14) (30,12) (33,19) (8,26) (2,28) (32,17) (10,3) (26,6) (30,14) (32,11) (26,27) (9,5) (7,23) (13,30) (9,1) (24,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph374",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,12) (15,6) (24,25) (7,12) (27,23) (27,14) (17,2) (25,4) (3,20) (9,22) (22,21) (5,6) (8,26) (0,14) (16,21) (18,24) (1,22) (26,14) (3,28) (18,10) (5,13) (0,24) (4,19) (2,22) (5,11) (21,5) (20,23) (23,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1371",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,21) (16,7) (23,18) (10,7) (0,2) (14,3) (1,25) (16,17) (12,19) (8,11) (20,15) (0,1) (1,7) (24,27) (9,25) (5,24) (6,8) (0,4) (3,26) (15,4) (9,13) (28,6) (2,4) (0,12) (8,3) (5,26) (9,22) (24,23) (17,12) (17,11) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph186",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,16) (0,26) (10,19) (17,8) (4,11) (17,5) (6,22) (13,20) (0,18) (8,20) (19,2) (17,15) (26,12) (7,6) (15,22) (15,19) (11,15) (12,15) (18,3) (7,21) (26,24) (17,25) (17,23) (7,1) (14,18) (4,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph332",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,22) (18,21) (20,4) (2,1) (7,28) (0,22) (22,25) (27,12) (17,14) (10,26) (13,22) (4,12) (10,7) (22,24) (19,21) (16,11) (4,19) (2,25) (5,8) (5,11) (11,9) (22,23) (23,6) (9,23) (19,15) (20,0) (19,3) (25,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1159",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,8) (0,4) (12,11) (17,13) (18,10) (0,2) (7,0) (5,4) (26,6) (17,24) (0,3) (16,2) (17,3) (21,11) (1,0) (14,25) (12,19) (7,5) (12,8) (16,20) (21,18) (22,17) (17,16) (20,10) (1,26) (26,7) (23,14) (9,7) (22,23) (15,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph922",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,15) (8,21) (22,23) (17,23) (10,21) (30,23) (31,32) (3,14) (3,1) (33,21) (25,32) (19,6) (5,10) (10,4) (20,15) (3,31) (13,16) (9,11) (28,1) (27,12) (5,20) (2,21) (24,0) (27,23) (4,30) (34,23) (6,0) (33,16) (21,29) (8,7) (9,18) (31,6) (0,26) (17,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1954",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,25) (9,24) (30,0) (1,25) (9,2) (3,0) (11,9) (34,14) (16,2) (22,8) (34,19) (3,8) (25,10) (15,23) (4,0) (34,13) (3,2) (8,14) (7,1) (12,32) (15,13) (21,25) (26,13) (0,2) (17,8) (14,20) (26,29) (0,1) (30,5) (33,21) (28,27) (31,21) (7,18) (7,5) (28,33) (7,6) (12,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1800",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,22) (32,5) (17,21) (33,7) (28,29) (14,12) (32,25) (30,6) (3,25) (2,10) (27,23) (0,1) (28,12) (20,31) (2,0) (29,4) (0,13) (13,29) (3,16) (10,3) (11,23) (24,16) (1,2) (15,1) (30,8) (20,32) (14,23) (22,18) (8,19) (9,17) (10,26) (3,21) (8,22) (14,8) (9,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1192",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (4,18) (7,23) (3,0) (26,23) (17,0) (0,26) (16,13) (17,12) (25,7) (0,2) (19,12) (2,26) (22,15) (12,15) (3,9) (6,5) (1,20) (9,21) (4,20) (1,13) (21,6) (6,22) (8,23) (11,23) (20,24) (0,1) (3,10) (14,8) (21,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph71",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,24) (25,6) (25,9) (14,13) (22,5) (3,2) (20,17) (18,14) (23,13) (15,18) (21,7) (15,10) (4,10) (16,8) (3,19) (4,3) (24,2) (21,8) (23,1) (13,0) (4,12) (18,21) (20,10) (13,6) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph358",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,0) (8,23) (19,5) (8,28) (3,1) (25,5) (7,12) (24,21) (25,24) (16,21) (7,6) (17,20) (15,9) (13,15) (22,3) (20,15) (28,5) (4,14) (6,26) (18,15) (2,21) (10,3) (27,22) (10,11) (8,6) (9,14) (16,10) (28,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1879",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,20) (7,22) (14,30) (3,18) (33,22) (16,2) (27,31) (0,17) (31,14) (26,28) (11,8) (14,10) (22,16) (11,19) (1,27) (0,3) (25,0) (29,8) (16,8) (13,18) (4,21) (27,23) (5,9) (9,17) (6,11) (27,28) (0,1) (12,9) (18,1) (0,4) (32,23) (0,2) (13,4) (16,5) (8,24) (15,14) (7,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph789",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,28) (21,14) (16,5) (20,22) (24,12) (23,3) (30,8) (31,1) (18,9) (26,21) (2,17) (14,15) (14,20) (11,5) (6,12) (4,21) (6,19) (32,12) (17,21) (27,6) (31,0) (21,10) (13,20) (17,27) (22,9) (14,0) (23,22) (25,4) (29,5) (4,5) (15,7) (30,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph940",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,16) (20,14) (4,8) (24,17) (20,17) (26,13) (28,11) (33,1) (7,31) (6,19) (22,18) (9,21) (20,29) (23,24) (16,28) (18,8) (29,10) (31,2) (6,5) (12,8) (7,28) (24,28) (9,13) (4,25) (26,15) (32,22) (8,34) (3,18) (5,2) (7,0) (25,15) (30,6) (32,27) (31,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph931",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (25,26) (32,10) (13,4) (7,15) (10,0) (2,17) (29,3) (20,34) (8,33) (16,28) (32,3) (21,18) (19,26) (17,20) (31,15) (4,22) (24,19) (18,33) (7,23) (20,3) (11,20) (7,20) (5,30) (31,28) (33,12) (19,33) (30,27) (4,23) (14,30) (18,13) (9,11) (6,34) (27,17) (14,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph61",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,24) (6,1) (7,23) (20,10) (1,17) (11,9) (18,2) (19,13) (8,14) (9,18) (6,4) (13,9) (18,3) (25,22) (20,14) (12,11) (6,16) (15,6) (0,15) (23,8) (25,6) (12,21) (0,3) (5,6) (14,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1810",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,17) (22,13) (26,6) (8,16) (29,15) (26,1) (8,12) (13,9) (27,1) (28,8) (0,33) (15,4) (9,25) (19,26) (20,8) (17,14) (33,31) (28,14) (13,21) (10,23) (2,0) (20,26) (7,2) (11,32) (12,0) (0,3) (1,0) (11,5) (8,3) (18,29) (11,30) (25,12) (6,4) (24,12) (14,7) (10,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1610",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,23) (27,8) (0,2) (18,16) (29,15) (10,13) (20,4) (12,17) (31,15) (26,18) (0,6) (28,22) (2,10) (7,29) (31,9) (14,31) (3,0) (1,2) (13,0) (22,24) (19,11) (27,3) (16,29) (26,2) (2,25) (26,24) (11,30) (5,30) (29,8) (8,23) (17,20) (4,15) (21,23) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph450",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,21) (22,21) (6,15) (22,17) (9,19) (0,12) (19,2) (13,23) (7,11) (4,24) (13,27) (17,2) (12,1) (10,5) (16,12) (23,19) (23,8) (25,6) (2,14) (24,12) (29,28) (15,26) (6,18) (3,6) (19,18) (20,8) (7,5) (4,7) (28,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1962",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,2) (18,30) (28,27) (1,0) (8,1) (5,11) (5,3) (16,19) (30,12) (7,10) (29,6) (28,34) (31,27) (28,20) (26,30) (33,24) (17,15) (4,29) (12,11) (21,6) (9,1) (33,0) (2,34) (32,24) (23,25) (10,23) (21,16) (34,22) (13,32) (0,2) (12,0) (14,7) (33,8) (9,22) (15,27) (3,21) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1971",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (12,22) (1,17) (21,10) (23,7) (22,13) (2,9) (4,12) (34,8) (27,26) (31,29) (20,28) (30,18) (1,19) (16,33) (16,11) (34,18) (13,28) (31,32) (30,12) (21,7) (5,24) (27,20) (0,17) (0,23) (25,24) (12,3) (20,15) (6,17) (6,9) (14,34) (26,17) (5,19) (5,11) (4,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph434",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,18) (28,4) (16,22) (23,29) (5,28) (23,4) (12,1) (17,8) (9,19) (4,14) (7,24) (29,10) (6,5) (0,14) (12,8) (21,7) (2,10) (12,27) (15,28) (24,22) (23,20) (27,24) (25,18) (7,3) (12,11) (13,18) (21,26) (17,9) (0,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1262",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,14) (1,0) (3,9) (14,17) (4,0) (1,22) (10,26) (24,10) (19,15) (22,19) (9,4) (8,14) (2,0) (18,14) (7,13) (7,11) (21,16) (27,1) (2,7) (20,25) (26,13) (17,23) (13,0) (3,0) (17,2) (6,20) (6,8) (12,14) (27,9) (16,5) (20,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph710",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,19) (25,4) (25,22) (32,29) (5,22) (1,6) (14,28) (21,26) (18,9) (2,10) (18,26) (30,13) (29,10) (6,31) (20,7) (13,6) (28,17) (6,24) (4,24) (19,9) (0,2) (16,4) (28,12) (23,32) (15,20) (12,9) (26,8) (11,27) (4,3) (9,20) (23,16) (26,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph435",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,29) (20,3) (5,1) (19,16) (5,24) (15,16) (20,21) (20,5) (26,6) (2,20) (22,17) (26,7) (18,28) (23,16) (19,26) (9,21) (27,10) (8,11) (16,28) (14,15) (29,2) (13,28) (0,18) (25,28) (20,12) (14,9) (15,8) (4,7) (10,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1998",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,13) (1,27) (10,17) (31,19) (0,3) (19,11) (2,0) (0,4) (33,15) (23,0) (21,5) (28,14) (10,9) (21,11) (26,14) (1,0) (21,32) (22,18) (28,9) (24,7) (15,28) (3,29) (11,24) (13,32) (2,32) (16,1) (18,34) (34,6) (22,25) (29,19) (28,1) (27,22) (24,14) (8,30) (8,4) (20,18) (12,30) (0,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph58",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,23) (14,11) (18,16) (7,23) (12,23) (17,11) (25,14) (0,21) (16,25) (20,1) (20,3) (3,21) (22,19) (25,19) (5,2) (10,16) (20,8) (9,12) (9,24) (21,14) (1,15) (6,21) (19,2) (14,13) (19,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph707",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,9) (5,3) (31,7) (20,1) (4,9) (5,23) (21,29) (12,1) (30,25) (2,30) (16,28) (18,9) (27,24) (7,12) (24,6) (29,6) (17,15) (22,4) (15,31) (31,5) (23,26) (11,26) (22,19) (16,31) (10,14) (32,6) (15,10) (19,11) (2,21) (22,13) (3,29) (28,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1136",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,14) (18,8) (0,5) (26,1) (17,13) (6,1) (20,8) (2,19) (17,4) (25,0) (11,3) (10,20) (9,16) (9,24) (19,11) (21,17) (3,7) (24,18) (15,12) (6,23) (22,13) (16,15) (10,2) (18,6) (7,22) (0,24) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph872",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,9) (18,32) (1,30) (16,31) (7,6) (28,15) (29,11) (4,3) (5,30) (22,14) (0,13) (11,3) (27,6) (19,12) (29,23) (2,9) (4,27) (19,20) (33,4) (6,26) (16,19) (8,33) (10,5) (1,7) (13,7) (13,18) (28,8) (23,17) (24,2) (23,24) (21,17) (32,31) (22,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1342",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,7) (5,3) (24,28) (12,18) (8,27) (22,16) (24,12) (0,4) (12,20) (0,3) (27,18) (24,5) (18,21) (22,20) (5,0) (11,5) (9,22) (0,23) (13,1) (6,22) (1,0) (16,2) (17,4) (2,0) (25,16) (17,0) (15,9) (10,3) (7,19) (9,26) (12,13) (7,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1512",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,13) (17,22) (8,28) (4,22) (7,26) (21,10) (25,4) (24,14) (21,13) (28,19) (16,15) (20,10) (1,12) (0,2) (19,5) (6,2) (1,0) (14,5) (23,21) (9,5) (13,14) (27,0) (30,7) (3,27) (6,10) (11,20) (3,22) (12,0) (29,10) (16,24) (30,4) (18,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph486",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (19,6) (3,4) (22,6) (7,12) (9,22) (14,4) (2,16) (29,0) (9,5) (2,20) (15,14) (3,18) (21,26) (21,13) (4,26) (29,8) (12,20) (1,3) (13,25) (16,10) (17,10) (22,21) (24,8) (24,10) (25,12) (28,7) (27,19) (14,11) (23,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph888",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,2) (4,29) (16,22) (8,17) (17,6) (1,21) (30,8) (16,32) (18,28) (7,19) (20,11) (12,31) (1,4) (20,22) (14,16) (26,4) (33,20) (19,5) (31,13) (17,9) (24,30) (11,2) (27,4) (26,10) (9,26) (3,9) (2,3) (21,23) (0,25) (18,7) (13,27) (15,5) (7,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph612",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,28) (14,10) (8,22) (26,11) (26,30) (1,2) (24,10) (17,14) (20,21) (26,21) (7,5) (31,30) (19,27) (22,12) (9,25) (14,15) (27,25) (6,28) (22,3) (4,18) (28,26) (18,5) (29,12) (14,26) (17,19) (31,5) (1,13) (2,6) (4,0) (12,27) (22,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1171",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,2) (4,5) (20,23) (22,5) (6,23) (10,21) (26,4) (25,21) (0,13) (3,9) (9,0) (18,4) (20,7) (23,9) (7,15) (24,2) (4,13) (25,11) (5,12) (6,17) (8,1) (21,26) (8,21) (20,14) (0,1) (16,21) (7,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph324",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,2) (23,22) (20,0) (22,17) (22,0) (28,7) (14,17) (19,4) (10,7) (9,23) (21,19) (22,25) (24,22) (6,23) (5,11) (2,1) (13,22) (4,20) (12,4) (7,25) (8,5) (19,3) (16,11) (21,18) (27,12) (11,9) (10,26) (19,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1500",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,20) (13,20) (24,0) (19,11) (13,9) (25,23) (0,2) (0,8) (1,11) (3,0) (0,27) (28,23) (2,1) (16,29) (10,17) (19,27) (11,12) (20,3) (12,22) (23,30) (0,1) (28,21) (12,29) (5,26) (3,12) (19,6) (7,14) (16,5) (18,26) (9,15) (16,7) (4,18) (10,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph263",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,2) (26,27) (12,13) (18,2) (20,9) (25,27) (2,26) (1,19) (23,24) (5,8) (21,16) (6,17) (15,8) (2,11) (23,12) (2,14) (9,4) (9,6) (9,26) (27,21) (21,7) (20,22) (10,21) (1,7) (14,0) (23,19) (14,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph889",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (30,9) (27,28) (0,15) (11,22) (17,31) (24,5) (5,33) (23,2) (16,2) (17,14) (0,28) (20,11) (7,2) (14,30) (32,31) (8,10) (4,10) (24,25) (12,23) (26,31) (29,10) (26,13) (1,17) (22,0) (7,26) (28,21) (24,2) (3,32) (18,8) (6,3) (4,15) (30,10) (26,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1714",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,13) (22,3) (19,8) (3,0) (11,13) (1,32) (27,15) (5,7) (25,26) (6,24) (31,5) (16,24) (20,0) (11,30) (27,28) (8,12) (1,0) (23,31) (27,22) (2,23) (29,2) (1,26) (6,5) (4,18) (1,9) (23,32) (13,3) (14,0) (18,22) (2,0) (17,28) (17,12) (1,21) (14,29) (19,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1648",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,7) (19,12) (5,29) (14,10) (11,30) (9,18) (23,1) (0,1) (31,5) (0,15) (3,9) (10,16) (7,30) (18,30) (1,19) (21,6) (31,4) (26,20) (3,0) (2,27) (22,19) (6,12) (2,10) (27,31) (28,31) (22,15) (5,25) (22,20) (0,11) (23,28) (8,24) (11,13) (2,0) (16,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph977",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,17) (24,10) (10,3) (28,8) (26,27) (11,17) (32,0) (30,28) (8,0) (11,24) (29,4) (34,22) (25,13) (31,8) (29,1) (34,10) (7,23) (20,15) (0,13) (8,4) (10,13) (24,21) (16,2) (6,15) (13,33) (18,7) (14,15) (12,1) (0,15) (22,5) (6,23) (19,30) (9,33) (3,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph833",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,33) (30,27) (21,16) (1,2) (20,1) (32,8) (25,11) (10,18) (7,3) (0,30) (17,8) (22,33) (14,2) (5,16) (29,28) (17,25) (4,23) (10,1) (15,30) (6,21) (13,6) (20,28) (21,22) (26,19) (22,15) (13,12) (32,20) (3,10) (23,20) (5,24) (26,0) (20,9) (31,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph721",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,29) (11,17) (16,6) (7,28) (0,13) (13,29) (21,4) (31,6) (8,18) (10,22) (20,13) (23,8) (4,23) (29,11) (32,19) (23,1) (15,9) (14,18) (24,7) (12,28) (26,10) (2,4) (19,3) (29,31) (24,8) (30,20) (27,1) (0,1) (16,15) (30,19) (26,32) (5,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph393",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,12) (10,16) (12,25) (19,26) (21,13) (15,10) (22,21) (4,14) (21,18) (26,4) (22,6) (16,2) (12,7) (27,7) (4,3) (10,24) (9,1) (8,28) (5,22) (20,2) (17,3) (6,19) (23,21) (24,8) (14,9) (0,3) (14,11) (13,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph507",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,19) (21,27) (14,25) (22,29) (8,28) (3,12) (3,11) (16,26) (9,5) (1,27) (15,3) (14,3) (27,7) (16,19) (29,27) (25,24) (8,16) (11,6) (30,0) (28,20) (4,16) (18,9) (8,10) (14,5) (10,5) (6,23) (19,0) (14,29) (25,17) (13,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1040",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,15) (5,11) (0,16) (5,18) (7,2) (21,9) (0,2) (5,17) (12,9) (7,14) (15,23) (4,5) (0,3) (16,14) (1,0) (3,5) (6,2) (10,24) (25,10) (21,8) (11,13) (0,24) (20,5) (0,19) (20,8) (18,1) (22,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1107",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,15) (18,15) (11,10) (17,4) (20,24) (16,1) (12,24) (7,26) (3,0) (25,3) (21,4) (15,8) (0,2) (26,13) (13,23) (2,9) (1,0) (10,24) (11,22) (25,6) (6,23) (0,24) (18,19) (18,5) (8,14) (15,25) (0,8) (23,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1666",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,25) (26,9) (1,8) (2,29) (0,24) (19,24) (20,9) (30,23) (0,1) (24,5) (27,18) (3,7) (17,22) (10,14) (13,4) (13,18) (15,0) (8,30) (2,0) (10,16) (21,11) (28,9) (23,4) (24,17) (1,15) (1,7) (12,14) (10,20) (21,18) (16,3) (27,2) (6,31) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph222",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,21) (11,15) (19,27) (22,1) (17,12) (12,22) (7,24) (11,18) (27,23) (21,24) (19,2) (8,6) (26,17) (4,26) (7,16) (0,6) (3,5) (13,24) (27,14) (7,17) (6,7) (24,10) (10,3) (18,19) (20,21) (27,25) (9,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1781",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (9,13) (11,6) (4,0) (32,27) (11,21) (14,8) (31,19) (21,5) (7,14) (10,15) (1,0) (22,12) (15,16) (11,29) (0,2) (13,24) (2,17) (31,5) (17,0) (20,30) (3,0) (18,5) (20,25) (3,24) (9,29) (25,1) (5,8) (27,0) (24,16) (13,26) (23,24) (30,5) (26,12) (25,2) (23,28) (12,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1910",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,25) (19,28) (26,22) (17,8) (24,12) (5,6) (27,5) (27,21) (30,31) (20,9) (15,2) (4,0) (5,12) (20,26) (12,2) (6,7) (13,32) (18,30) (0,1) (1,10) (34,12) (28,21) (2,0) (33,6) (26,14) (3,0) (15,13) (10,11) (23,13) (16,4) (25,5) (0,9) (20,8) (16,3) (20,21) (33,29) (4,6) (1,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph415",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,3) (27,4) (13,3) (20,27) (16,19) (9,5) (16,25) (27,0) (14,3) (28,14) (28,18) (10,8) (3,11) (17,9) (14,5) (29,19) (29,26) (14,24) (10,5) (16,8) (27,8) (2,16) (11,6) (1,19) (15,25) (25,23) (21,29) (12,10) (22,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph429",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,15) (9,13) (27,7) (5,12) (14,2) (19,26) (1,15) (0,20) (9,6) (2,6) (11,26) (16,8) (8,4) (10,8) (17,21) (5,7) (24,12) (3,22) (17,10) (29,23) (29,25) (26,2) (11,8) (22,26) (20,18) (15,26) (18,29) (23,2) (28,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph634",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,7) (29,23) (13,18) (31,4) (2,24) (27,4) (6,27) (30,5) (29,1) (16,31) (20,19) (2,9) (11,8) (17,21) (7,13) (14,22) (8,28) (25,9) (28,15) (5,10) (4,22) (19,16) (12,19) (7,1) (23,24) (4,3) (23,17) (11,3) (0,13) (26,6) (30,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph439",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,1) (11,8) (26,18) (27,11) (1,12) (7,1) (2,17) (24,0) (24,22) (23,15) (20,25) (9,16) (17,21) (25,22) (12,6) (10,13) (24,29) (21,19) (9,23) (26,5) (11,0) (15,14) (15,29) (24,28) (2,25) (26,6) (4,18) (20,1) (11,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph307",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,15) (12,3) (27,24) (18,7) (17,20) (14,1) (3,28) (23,21) (23,8) (25,3) (24,20) (16,19) (27,22) (15,13) (2,22) (13,7) (11,5) (16,9) (10,14) (26,6) (18,19) (4,23) (24,25) (23,0) (14,17) (21,10) (11,26) (17,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph166",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,9) (3,26) (3,4) (26,19) (23,13) (10,0) (0,23) (11,13) (11,15) (11,14) (14,25) (6,9) (26,11) (17,0) (8,17) (13,7) (21,8) (5,2) (20,19) (21,12) (15,16) (13,9) (13,22) (24,0) (5,8) (1,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1232",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,3) (25,23) (15,7) (16,2) (23,24) (25,8) (22,3) (5,8) (11,8) (26,20) (2,4) (1,19) (20,1) (0,1) (9,13) (2,19) (9,18) (21,25) (17,15) (27,23) (10,14) (9,27) (4,8) (0,15) (10,0) (3,9) (12,2) (13,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph848",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,19) (0,22) (23,16) (22,17) (14,23) (20,24) (9,0) (3,5) (30,5) (33,9) (4,15) (4,27) (6,29) (13,33) (20,13) (2,33) (19,10) (26,21) (19,25) (1,12) (24,18) (3,24) (9,28) (11,14) (16,3) (27,32) (17,6) (22,7) (1,8) (10,32) (24,1) (23,31) (6,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1952",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,33) (4,13) (32,3) (33,18) (0,10) (18,21) (19,24) (28,16) (9,11) (20,17) (17,27) (7,15) (17,2) (14,30) (34,20) (23,7) (26,25) (19,33) (10,32) (1,14) (19,26) (30,5) (29,3) (0,1) (23,4) (3,20) (31,15) (6,34) (28,31) (13,18) (22,4) (20,7) (8,33) (11,20) (27,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1216",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (8,16) (26,15) (4,8) (22,26) (9,6) (11,8) (17,10) (2,26) (12,24) (11,26) (15,7) (17,21) (6,2) (22,3) (20,0) (23,2) (0,1) (9,13) (0,2) (18,20) (10,8) (27,18) (7,5) (23,20) (26,19) (7,25) (14,2) (15,1) (12,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1513",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,9) (7,11) (10,5) (4,24) (18,6) (22,17) (0,12) (17,2) (8,20) (30,2) (16,21) (22,21) (27,15) (1,12) (28,25) (6,15) (19,26) (23,8) (6,3) (4,7) (19,23) (6,25) (0,2) (18,19) (12,24) (14,2) (30,28) (1,0) (23,13) (7,5) (13,29) (12,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph323",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,5) (6,27) (1,8) (20,7) (7,24) (20,23) (21,10) (7,18) (9,23) (9,0) (17,27) (3,9) (21,19) (17,2) (4,5) (5,15) (25,11) (28,14) (23,6) (21,4) (27,22) (13,0) (13,4) (4,28) (26,2) (8,21) (16,20) (12,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1725",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,8) (6,32) (13,25) (10,12) (12,25) (3,23) (32,15) (30,26) (5,31) (29,21) (0,1) (14,31) (20,1) (7,24) (5,25) (28,31) (8,9) (12,29) (29,23) (8,15) (2,11) (5,2) (24,30) (19,13) (31,22) (14,0) (0,2) (24,27) (6,16) (24,4) (1,17) (16,7) (17,26) (14,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph853",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,0) (27,1) (3,4) (1,26) (24,13) (9,30) (27,19) (14,32) (5,7) (11,13) (10,24) (8,2) (24,18) (4,16) (20,1) (31,15) (30,0) (13,27) (7,31) (14,17) (33,31) (31,28) (1,29) (17,23) (6,20) (14,28) (33,1) (6,25) (22,28) (8,28) (16,1) (24,0) (12,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1938",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (19,13) (0,3) (10,29) (1,9) (4,26) (0,27) (21,17) (21,8) (1,0) (8,0) (28,14) (5,2) (33,4) (25,17) (3,20) (5,25) (10,24) (32,9) (11,22) (20,5) (12,4) (3,29) (14,9) (6,16) (19,21) (22,13) (5,30) (7,8) (21,18) (26,30) (16,26) (32,34) (9,15) (4,23) (29,31) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1264",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,12) (12,11) (3,14) (0,3) (6,23) (4,0) (14,7) (23,24) (25,17) (18,23) (1,15) (6,12) (0,2) (10,17) (4,17) (14,19) (6,1) (2,19) (27,16) (15,9) (14,26) (16,10) (5,9) (15,25) (15,8) (0,1) (2,17) (13,7) (18,21) (20,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph904",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,17) (33,21) (11,9) (8,21) (34,23) (26,0) (4,30) (19,6) (8,7) (23,17) (30,23) (1,3) (16,13) (21,2) (10,21) (28,1) (27,12) (31,32) (31,6) (9,18) (31,3) (27,23) (10,4) (16,33) (21,29) (5,20) (6,0) (10,5) (25,32) (0,24) (22,23) (14,3) (20,15) (15,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph773",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,16) (18,7) (3,28) (30,0) (11,15) (29,15) (23,20) (2,17) (3,26) (5,27) (0,22) (19,16) (21,14) (23,25) (25,6) (15,31) (6,9) (30,1) (12,4) (4,5) (18,21) (31,4) (16,8) (32,25) (21,8) (16,17) (11,24) (27,26) (9,14) (10,12) (13,4) (28,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1196",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,6) (2,14) (6,3) (23,13) (19,23) (25,15) (11,7) (15,6) (12,0) (5,7) (18,26) (19,18) (21,16) (8,20) (7,4) (17,2) (12,16) (24,12) (2,19) (12,1) (19,9) (21,22) (1,0) (24,4) (10,5) (23,8) (22,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph606",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,3) (0,20) (23,6) (0,25) (30,10) (13,8) (22,11) (24,22) (9,26) (15,4) (30,26) (4,10) (14,17) (11,18) (10,27) (26,16) (31,17) (21,2) (1,17) (3,5) (19,28) (24,31) (8,10) (26,7) (12,2) (2,24) (14,28) (0,15) (28,23) (29,31) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1018",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,0) (0,2) (12,3) (13,14) (21,20) (11,24) (4,24) (17,16) (20,9) (24,25) (7,10) (23,8) (13,3) (18,24) (22,2) (23,9) (14,0) (16,23) (12,22) (1,0) (10,0) (0,5) (2,15) (3,16) (1,25) (19,23) (6,17) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1784",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,26) (27,3) (24,21) (17,12) (19,2) (6,11) (19,10) (4,1) (30,13) (6,16) (15,30) (9,20) (18,25) (29,11) (14,3) (23,14) (5,23) (25,8) (24,32) (0,15) (28,17) (16,17) (10,12) (16,1) (22,4) (1,0) (5,21) (5,9) (18,23) (31,32) (7,6) (1,13) (18,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph471",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (24,29) (27,13) (12,6) (28,25) (11,26) (16,25) (21,3) (12,24) (14,18) (21,4) (0,2) (22,8) (5,9) (7,6) (21,14) (27,15) (6,25) (8,7) (26,14) (26,19) (25,11) (20,14) (5,2) (12,5) (17,23) (23,19) (15,6) (14,10) (1,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1949",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,9) (26,6) (26,1) (29,19) (4,6) (8,10) (16,14) (20,8) (7,11) (0,1) (28,8) (22,13) (2,0) (8,12) (26,21) (4,15) (7,2) (23,13) (8,18) (26,20) (12,25) (8,3) (17,14) (11,32) (25,9) (14,28) (29,1) (24,10) (0,34) (27,12) (0,3) (32,33) (34,5) (15,30) (33,17) (31,11) (0,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1115",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,25) (0,4) (1,7) (25,3) (7,6) (11,8) (7,16) (11,17) (15,4) (5,26) (26,3) (0,12) (3,13) (20,2) (21,9) (5,24) (14,23) (22,24) (1,0) (12,17) (1,23) (18,12) (10,9) (19,15) (5,0) (17,16) (4,2) (24,8) (3,0) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph86",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (8,15) (23,4) (14,1) (19,10) (12,18) (18,21) (13,15) (7,13) (9,3) (7,16) (22,24) (21,11) (25,24) (8,23) (11,5) (5,17) (23,0) (24,20) (17,20) (22,2) (19,3) (10,14) (17,14) (23,25) (16,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph291",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,12) (11,0) (6,17) (3,12) (12,24) (11,13) (19,1) (8,22) (2,8) (17,15) (9,27) (4,27) (7,25) (12,20) (21,11) (24,17) (19,26) (23,26) (17,22) (18,0) (0,4) (7,5) (1,12) (5,16) (18,16) (13,10) (11,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph601",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (5,22) (8,27) (8,28) (0,13) (23,26) (10,4) (13,31) (0,29) (30,13) (15,12) (9,1) (17,25) (6,21) (15,0) (30,18) (7,16) (3,14) (1,29) (13,22) (16,2) (28,26) (24,11) (7,23) (19,15) (6,15) (10,3) (8,0) (8,4) (20,24) (17,11) (24,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph42",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,8) (6,3) (4,7) (7,11) (12,20) (22,17) (8,18) (19,25) (19,2) (5,7) (6,13) (12,0) (5,10) (9,19) (23,13) (21,22) (6,15) (14,2) (24,15) (17,2) (23,19) (16,21) (12,16) (1,12) (4,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1600",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,11) (30,18) (14,10) (30,11) (0,11) (23,28) (30,7) (25,5) (28,31) (19,12) (16,10) (8,7) (0,3) (8,24) (15,22) (17,16) (29,5) (6,12) (31,5) (0,15) (31,27) (23,1) (4,31) (20,26) (0,1) (18,9) (9,3) (20,22) (19,22) (27,2) (21,6) (10,2) (1,19) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph971",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,24) (20,29) (12,13) (17,13) (14,27) (25,9) (8,7) (24,8) (29,30) (29,1) (33,30) (16,3) (1,2) (5,23) (11,24) (19,12) (26,19) (28,10) (31,1) (3,26) (5,6) (11,20) (2,10) (0,31) (11,18) (32,22) (22,9) (2,15) (21,19) (30,12) (28,14) (34,20) (29,4) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1868",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (9,30) (14,31) (28,17) (27,6) (24,20) (7,20) (9,29) (14,18) (26,3) (7,11) (29,2) (1,32) (2,32) (20,22) (25,17) (23,18) (22,5) (32,12) (3,19) (13,26) (13,4) (24,27) (2,21) (15,8) (22,17) (33,16) (25,3) (1,0) (25,23) (15,1) (4,16) (6,8) (26,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1394",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,1) (5,22) (10,22) (18,11) (8,11) (19,27) (21,9) (25,20) (24,6) (24,27) (14,4) (25,18) (12,13) (24,13) (2,1) (17,28) (28,12) (22,15) (17,26) (11,19) (3,14) (0,2) (0,16) (14,19) (4,7) (19,15) (21,3) (1,0) (0,23) (16,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph927",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,4) (34,7) (32,5) (11,22) (32,29) (21,16) (31,12) (26,33) (7,3) (19,1) (12,8) (14,18) (16,26) (24,4) (2,33) (4,6) (22,20) (6,1) (25,10) (12,7) (6,27) (33,13) (34,27) (6,17) (16,9) (26,1) (9,15) (19,20) (29,24) (28,12) (6,18) (23,17) (0,2) (20,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph295",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,6) (4,21) (27,4) (4,5) (11,7) (9,21) (9,10) (16,1) (23,11) (26,2) (22,24) (9,7) (23,26) (16,12) (8,17) (24,26) (14,20) (0,10) (19,25) (0,19) (12,15) (3,14) (17,13) (26,15) (5,18) (0,17) (21,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph496",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,15) (26,19) (23,3) (19,21) (28,17) (2,16) (29,0) (17,27) (26,11) (4,5) (11,12) (21,3) (25,24) (11,2) (28,3) (8,29) (13,11) (5,18) (15,7) (20,4) (18,9) (6,27) (23,10) (5,25) (28,14) (18,1) (22,12) (1,19) (29,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1338",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,22) (23,0) (12,20) (0,17) (6,22) (7,19) (18,12) (13,1) (5,11) (0,5) (13,12) (5,24) (27,18) (1,0) (27,8) (24,12) (3,0) (5,3) (17,4) (16,25) (18,21) (9,15) (3,10) (7,3) (0,4) (16,22) (16,2) (22,20) (24,28) (9,26) (14,7) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1711",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,0) (19,15) (9,23) (11,7) (7,3) (31,20) (26,4) (10,9) (5,29) (18,24) (0,30) (11,27) (16,27) (17,13) (11,22) (14,28) (18,2) (8,26) (32,14) (6,31) (4,1) (19,29) (13,2) (12,17) (23,0) (10,2) (26,28) (0,2) (17,21) (25,31) (1,0) (7,6) (25,10) (15,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph699",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,13) (31,19) (4,22) (14,24) (9,1) (1,15) (25,4) (7,17) (5,29) (5,18) (10,25) (25,1) (16,8) (15,17) (23,4) (3,25) (8,30) (27,28) (19,29) (20,0) (22,26) (6,17) (11,13) (2,18) (6,27) (21,1) (0,15) (12,16) (24,10) (8,19) (7,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1503",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,8) (12,18) (5,10) (4,0) (12,0) (11,14) (19,21) (30,28) (4,16) (2,0) (21,0) (0,1) (27,22) (15,24) (8,2) (7,29) (7,17) (15,8) (3,0) (21,3) (9,21) (11,23) (22,26) (5,11) (19,27) (25,14) (19,4) (1,15) (4,14) (0,17) (11,13) (16,6) (20,25) (10,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1521",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,27) (1,4) (5,6) (29,11) (25,3) (24,26) (25,14) (17,29) (23,14) (28,26) (27,13) (1,0) (7,11) (10,16) (25,19) (2,5) (3,1) (17,10) (21,17) (21,0) (25,17) (9,29) (14,18) (10,8) (13,18) (25,15) (27,12) (14,30) (2,19) (26,16) (22,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph112",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,24) (1,20) (1,21) (14,23) (8,4) (17,20) (3,6) (24,10) (7,19) (3,10) (7,16) (24,23) (12,16) (13,5) (21,18) (25,8) (16,17) (15,1) (23,1) (11,17) (0,2) (14,4) (26,9) (19,9) (13,25) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph239",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,18) (3,12) (24,23) (27,0) (16,19) (9,13) (0,22) (17,10) (20,13) (16,7) (14,7) (1,2) (21,12) (11,19) (25,5) (8,0) (19,6) (26,18) (12,11) (26,12) (10,15) (27,23) (20,23) (15,9) (20,3) (1,11) (16,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph68",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,11) (4,22) (8,3) (24,12) (9,14) (20,14) (7,25) (23,15) (3,0) (3,24) (8,16) (2,19) (19,1) (8,7) (23,18) (21,12) (16,10) (8,13) (6,20) (9,22) (24,5) (2,21) (17,9) (23,12) (21,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1287",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,12) (27,6) (13,25) (27,19) (5,0) (3,2) (27,21) (9,25) (3,0) (0,13) (23,18) (14,13) (16,8) (11,24) (10,15) (21,8) (14,18) (1,23) (6,13) (20,3) (24,5) (3,4) (26,2) (0,1) (7,21) (22,10) (20,17) (2,0) (15,18) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph290",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,11) (4,17) (10,20) (23,6) (9,15) (17,25) (6,12) (24,23) (16,10) (9,5) (27,16) (25,15) (4,0) (10,17) (15,8) (2,19) (22,12) (14,26) (14,7) (14,19) (13,7) (1,6) (1,15) (18,23) (14,3) (21,18) (17,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph751",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,17) (0,10) (7,21) (22,16) (24,32) (8,16) (13,24) (5,1) (25,7) (17,13) (17,30) (9,23) (11,18) (29,14) (14,20) (10,31) (23,16) (4,7) (10,9) (2,6) (28,15) (19,29) (25,27) (3,15) (17,5) (18,19) (28,16) (25,26) (12,4) (20,22) (4,0) (1,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph216",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,1) (15,19) (8,6) (2,7) (25,20) (7,11) (5,16) (10,26) (21,16) (0,13) (17,2) (13,26) (27,1) (9,27) (22,19) (14,17) (12,14) (18,14) (20,15) (9,3) (24,10) (4,9) (17,23) (13,7) (14,8) (20,6) (14,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1522",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,0) (17,10) (7,28) (13,30) (11,8) (0,4) (23,29) (0,3) (20,0) (3,22) (21,26) (6,9) (19,8) (22,17) (2,0) (15,26) (23,2) (24,26) (8,4) (29,20) (11,26) (10,8) (6,2) (20,18) (5,7) (15,1) (27,29) (26,2) (18,30) (12,25) (9,14) (12,5) (16,2) (7,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1974",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,0) (18,14) (1,31) (2,0) (17,15) (0,18) (9,21) (5,26) (0,11) (9,32) (14,28) (26,16) (19,22) (25,19) (34,5) (30,16) (30,4) (21,24) (12,26) (8,14) (1,9) (27,1) (16,13) (19,23) (14,15) (2,23) (19,14) (3,30) (29,18) (16,23) (6,18) (29,1) (29,33) (28,10) (7,26) (20,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph196",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,2) (8,10) (0,20) (10,5) (3,5) (20,10) (22,16) (10,9) (18,22) (11,15) (24,12) (6,25) (2,11) (15,1) (16,0) (2,22) (17,4) (7,6) (25,17) (25,5) (14,10) (13,9) (15,21) (11,23) (19,0) (14,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph108",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,25) (5,23) (24,20) (3,8) (7,2) (0,14) (0,7) (12,17) (16,13) (8,23) (25,21) (10,15) (19,4) (20,0) (11,5) (26,13) (9,16) (11,14) (11,15) (1,18) (1,17) (22,13) (14,12) (1,6) (26,2) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1492",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,2) (11,26) (7,26) (18,15) (27,23) (6,23) (15,8) (0,24) (1,16) (25,3) (0,8) (4,21) (24,12) (6,25) (2,9) (15,25) (24,21) (14,8) (13,29) (18,20) (5,18) (13,27) (17,29) (28,17) (0,3) (11,10) (22,23) (4,19) (0,2) (24,10) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1446",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,25) (27,6) (29,12) (5,24) (3,0) (4,9) (16,8) (0,1) (13,1) (10,13) (9,22) (2,12) (15,11) (8,1) (0,2) (23,15) (20,25) (24,3) (18,28) (12,17) (0,27) (6,16) (28,9) (4,24) (28,7) (11,18) (25,19) (4,16) (3,19) (15,14) (21,26) (29,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph893",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (26,0) (20,16) (32,3) (24,2) (15,2) (16,14) (18,12) (10,26) (4,17) (30,9) (6,3) (6,19) (24,28) (31,32) (18,15) (23,29) (9,11) (8,19) (9,19) (29,0) (27,5) (4,33) (9,1) (8,10) (21,2) (13,9) (1,14) (22,30) (17,15) (18,14) (7,19) (21,25) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph993",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,5) (13,31) (12,18) (6,13) (1,2) (23,31) (16,11) (5,24) (18,9) (20,5) (3,19) (10,14) (21,33) (28,7) (28,15) (30,16) (21,2) (15,17) (21,8) (27,14) (23,27) (25,12) (28,0) (17,1) (2,32) (29,10) (4,19) (14,3) (34,21) (18,4) (6,2) (27,30) (26,8) (22,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph80",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,25) (1,5) (25,2) (0,11) (6,12) (9,23) (15,6) (21,16) (0,24) (15,13) (25,24) (18,17) (15,19) (1,20) (9,14) (17,2) (4,18) (8,13) (12,1) (3,11) (7,11) (21,22) (23,11) (24,22) (1,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph460",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (25,4) (14,27) (28,14) (0,14) (9,23) (6,5) (20,23) (4,19) (21,16) (2,22) (5,21) (17,2) (23,27) (22,1) (12,7) (29,25) (11,5) (21,22) (29,3) (12,6) (6,15) (24,26) (26,8) (3,20) (10,18) (13,5) (0,24) (18,24) (22,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph780",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,21) (5,20) (1,0) (1,25) (14,10) (6,20) (16,5) (16,17) (2,17) (28,9) (7,26) (31,9) (27,14) (23,14) (23,12) (10,8) (22,11) (6,1) (11,13) (10,15) (30,0) (19,25) (3,29) (17,13) (3,24) (24,26) (25,4) (15,24) (18,23) (0,32) (28,8) (23,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph581",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,30) (1,18) (14,26) (19,26) (5,12) (25,17) (10,5) (16,27) (18,23) (6,7) (24,19) (15,27) (30,12) (25,11) (20,14) (30,28) (7,8) (14,22) (30,3) (9,21) (4,21) (15,6) (8,23) (2,0) (26,11) (21,14) (25,6) (5,2) (25,29) (13,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1463",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,9) (25,28) (14,15) (1,12) (20,7) (0,29) (9,6) (7,1) (5,27) (27,21) (24,27) (0,2) (28,0) (25,20) (12,4) (14,28) (0,1) (25,22) (21,2) (2,26) (8,13) (4,5) (1,19) (28,10) (15,17) (16,25) (11,4) (18,9) (23,29) (3,0) (7,8) (0,4) (10,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph145",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,10) (20,16) (17,16) (7,0) (17,3) (9,7) (17,13) (5,4) (26,1) (21,11) (16,2) (8,12) (24,17) (23,14) (10,20) (7,5) (22,17) (26,8) (18,21) (7,26) (26,6) (19,12) (8,15) (14,25) (22,23) (11,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph967",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,10) (24,28) (10,2) (15,4) (31,9) (2,27) (19,11) (24,34) (26,32) (29,16) (21,20) (2,1) (33,11) (0,13) (25,23) (30,8) (26,18) (17,31) (31,22) (7,29) (33,14) (29,15) (24,22) (6,0) (4,20) (28,15) (5,30) (18,16) (2,26) (23,8) (12,17) (27,3) (19,23) (29,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1091",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,3) (3,23) (0,2) (1,4) (5,13) (5,14) (9,24) (22,18) (15,13) (6,0) (7,23) (8,14) (19,15) (22,25) (15,21) (0,11) (12,19) (0,1) (23,22) (11,2) (15,22) (4,2) (11,10) (4,20) (7,17) (9,5) (7,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1098",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,1) (9,11) (10,16) (25,15) (2,24) (22,1) (5,24) (5,19) (2,0) (8,21) (5,14) (4,17) (16,25) (3,18) (23,18) (3,4) (8,5) (20,21) (15,3) (9,6) (15,7) (0,4) (9,17) (1,0) (24,6) (12,25) (13,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1929",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,17) (22,8) (12,28) (32,6) (8,31) (20,32) (10,3) (23,29) (26,16) (22,32) (1,18) (27,10) (4,0) (14,8) (9,5) (30,7) (8,24) (16,3) (14,23) (22,19) (0,1) (33,20) (11,33) (0,2) (32,25) (13,23) (10,2) (12,14) (30,28) (2,1) (13,0) (15,29) (21,3) (3,0) (3,25) (21,17) (34,5) (29,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1453",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (10,21) (25,20) (23,4) (6,21) (12,20) (21,24) (26,0) (27,14) (5,6) (18,13) (29,6) (29,9) (12,15) (8,23) (7,3) (0,2) (8,16) (28,13) (0,17) (28,22) (0,3) (26,2) (15,22) (27,24) (1,20) (4,28) (11,23) (19,1) (26,29) (1,0) (12,17) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1003",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (23,21) (0,6) (0,3) (11,13) (11,18) (24,10) (3,4) (17,22) (14,25) (6,7) (18,21) (7,17) (6,5) (2,19) (20,12) (0,1) (17,12) (22,1) (7,15) (14,8) (14,18) (10,3) (24,19) (19,18) (24,7) (16,21) (9,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph198",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,18) (24,1) (20,4) (16,22) (21,1) (4,19) (7,17) (3,13) (24,6) (11,1) (17,23) (9,4) (26,14) (0,2) (21,25) (8,12) (7,15) (4,7) (23,14) (4,1) (15,0) (22,23) (5,3) (3,17) (4,12) (10,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1542",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,14) (6,0) (17,10) (6,23) (29,11) (1,15) (30,23) (15,0) (24,26) (25,24) (21,25) (27,13) (24,20) (20,19) (6,28) (26,22) (16,8) (1,0) (19,7) (4,20) (29,17) (5,3) (18,25) (22,29) (9,12) (6,14) (27,2) (12,21) (4,2) (20,3) (22,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1340",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,24) (3,0) (13,10) (28,5) (8,19) (18,4) (28,10) (4,0) (8,25) (17,6) (3,24) (18,20) (3,26) (15,16) (1,0) (7,16) (11,16) (25,1) (3,14) (9,27) (8,22) (6,12) (2,0) (4,19) (28,9) (12,11) (3,21) (0,21) (1,2) (23,13) (26,8) (9,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1564",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,30) (5,30) (30,16) (17,0) (2,8) (13,14) (17,18) (27,30) (28,6) (0,2) (3,12) (21,11) (24,12) (22,26) (11,13) (12,20) (27,9) (7,5) (7,26) (17,4) (29,25) (7,12) (0,3) (30,10) (8,22) (29,16) (19,1) (0,11) (15,11) (19,28) (4,0) (1,12) (17,24) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1687",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,30) (7,12) (19,31) (2,0) (16,20) (28,12) (0,1) (19,8) (28,4) (12,1) (6,3) (8,6) (22,15) (12,10) (13,30) (18,19) (11,18) (26,21) (14,25) (17,18) (2,11) (6,25) (31,0) (0,26) (4,29) (22,18) (0,3) (9,2) (5,13) (3,23) (28,16) (24,28) (27,13) (23,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph941",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,7) (4,6) (17,14) (26,34) (26,16) (23,7) (1,2) (17,23) (15,20) (12,0) (34,33) (8,29) (22,30) (1,18) (1,4) (13,2) (16,25) (11,12) (21,28) (4,34) (3,1) (15,28) (27,12) (34,15) (5,27) (24,19) (32,34) (6,11) (8,31) (23,9) (8,6) (30,4) (3,10) (19,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1205",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,15) (7,12) (27,23) (14,3) (6,10) (16,21) (7,19) (17,18) (17,4) (15,9) (13,6) (0,8) (1,25) (19,22) (2,8) (0,1) (26,0) (9,3) (2,0) (5,15) (24,8) (27,25) (7,4) (11,10) (16,0) (21,20) (26,6) (20,17) (25,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph339",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,27) (3,15) (1,20) (11,13) (9,1) (16,19) (14,10) (9,25) (19,8) (19,18) (8,12) (4,24) (6,22) (28,8) (5,14) (1,5) (15,28) (3,21) (5,3) (13,15) (21,23) (17,13) (7,13) (6,20) (24,5) (2,0) (26,14) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1811",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,19) (29,16) (11,31) (9,14) (32,12) (24,17) (28,10) (25,17) (6,10) (2,0) (16,2) (11,22) (7,27) (30,0) (25,0) (3,33) (18,33) (22,19) (23,21) (26,24) (16,13) (20,21) (28,23) (1,12) (32,5) (8,15) (28,1) (7,1) (30,10) (4,15) (25,14) (29,15) (30,2) (0,3) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph569",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,13) (0,21) (2,13) (2,5) (19,1) (29,30) (12,19) (30,27) (12,16) (18,12) (9,18) (25,15) (1,25) (10,11) (22,30) (15,23) (4,11) (17,23) (30,8) (8,10) (8,26) (24,3) (14,7) (17,6) (28,25) (17,0) (21,13) (0,29) (3,0) (14,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph160",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,18) (8,22) (5,18) (9,13) (5,3) (26,2) (24,0) (0,16) (25,15) (7,14) (10,24) (8,20) (5,19) (11,14) (12,7) (9,21) (11,5) (21,0) (3,0) (5,4) (17,16) (16,15) (10,26) (6,2) (5,20) (23,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1211",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,5) (0,15) (20,2) (16,19) (23,18) (4,17) (25,11) (8,24) (10,17) (4,13) (27,20) (0,19) (0,21) (2,22) (2,0) (12,27) (20,6) (0,3) (26,1) (25,4) (1,0) (25,8) (16,23) (14,15) (6,25) (23,9) (7,16) (6,19) (0,4) (3,24) (18,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1742",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,6) (9,5) (24,20) (19,10) (3,16) (11,1) (14,8) (24,18) (24,1) (5,3) (2,0) (21,25) (1,0) (32,13) (32,26) (16,23) (14,4) (15,19) (27,9) (0,22) (12,23) (17,6) (27,4) (20,13) (1,7) (10,30) (23,29) (3,24) (9,0) (31,13) (22,17) (28,6) (18,19) (22,2) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1443",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,0) (7,16) (24,25) (0,27) (19,6) (26,17) (11,0) (2,4) (13,2) (9,14) (7,25) (21,16) (15,9) (20,15) (24,29) (28,18) (13,18) (8,22) (15,25) (6,25) (16,5) (0,1) (22,5) (11,29) (4,25) (13,3) (23,16) (1,5) (12,20) (13,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1842",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,7) (0,1) (28,1) (10,16) (30,24) (16,18) (32,10) (10,11) (27,33) (14,32) (5,20) (21,31) (23,21) (6,29) (5,13) (13,10) (30,1) (2,11) (7,22) (2,0) (25,19) (4,3) (9,22) (0,17) (8,19) (0,29) (12,10) (11,15) (26,30) (0,33) (15,4) (19,21) (25,1) (23,29) (28,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1081",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,12) (3,2) (6,10) (4,0) (22,5) (23,14) (23,12) (4,14) (24,9) (17,24) (14,7) (21,1) (20,21) (3,22) (2,23) (1,8) (6,20) (17,3) (25,16) (16,13) (0,1) (11,13) (14,8) (19,11) (25,10) (5,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1119",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,14) (12,3) (20,9) (10,8) (0,5) (14,13) (15,2) (10,23) (3,16) (12,23) (22,26) (26,7) (11,0) (1,25) (24,4) (2,22) (24,0) (23,21) (26,9) (23,18) (24,16) (1,0) (17,16) (3,26) (6,17) (20,19) (13,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1224",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,4) (19,15) (0,3) (9,19) (14,23) (19,26) (0,2) (6,21) (26,18) (0,13) (8,6) (25,10) (24,16) (0,1) (11,9) (8,1) (20,12) (26,5) (7,0) (1,12) (19,27) (17,20) (14,0) (25,26) (3,17) (4,20) (2,5) (22,12) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph868",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,5) (15,12) (23,17) (21,22) (15,7) (0,33) (0,6) (26,31) (19,32) (32,14) (22,16) (23,9) (8,2) (2,10) (22,13) (28,19) (24,16) (29,14) (29,18) (25,14) (33,5) (27,13) (22,20) (30,26) (3,1) (29,26) (20,14) (7,21) (4,13) (25,17) (10,15) (1,11) (9,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1534",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (16,22) (14,7) (30,21) (0,4) (9,27) (0,1) (11,5) (9,22) (22,21) (23,18) (0,25) (0,17) (1,13) (2,0) (20,28) (29,18) (8,27) (3,0) (12,13) (2,16) (3,10) (26,16) (12,24) (6,22) (17,4) (12,18) (7,3) (22,24) (7,19) (3,5) (12,20) (9,15) (24,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1575",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,2) (15,28) (28,19) (9,13) (9,8) (28,18) (21,20) (11,22) (23,4) (15,6) (1,0) (1,21) (22,3) (1,4) (18,12) (24,25) (2,0) (17,23) (2,11) (30,20) (25,14) (8,11) (5,2) (10,18) (0,3) (20,16) (30,29) (7,21) (26,27) (0,6) (18,14) (8,15) (9,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph82",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,2) (17,9) (25,1) (25,22) (11,25) (18,6) (20,10) (24,19) (16,4) (21,17) (13,8) (21,18) (3,23) (25,8) (18,3) (12,18) (15,5) (21,20) (7,17) (16,15) (0,13) (2,5) (14,25) (10,1) (24,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph605",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,17) (16,6) (21,5) (19,10) (15,0) (16,17) (30,13) (1,4) (23,18) (18,19) (5,9) (3,14) (14,23) (1,16) (18,25) (29,11) (7,6) (5,23) (17,12) (21,24) (20,9) (15,30) (24,31) (8,25) (2,19) (6,11) (22,4) (25,26) (3,27) (1,13) (12,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph574",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,6) (1,6) (3,0) (8,28) (25,24) (9,23) (28,26) (14,25) (30,6) (6,5) (9,13) (1,20) (2,18) (19,25) (6,4) (21,14) (17,6) (27,18) (20,10) (22,12) (14,29) (30,8) (18,3) (30,16) (30,11) (12,11) (23,7) (9,27) (0,15) (13,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1830",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,0) (21,6) (4,27) (9,19) (0,3) (8,10) (14,23) (22,31) (1,4) (32,21) (27,29) (32,24) (1,13) (10,31) (12,27) (14,13) (8,4) (6,15) (15,17) (32,25) (0,4) (28,13) (3,18) (7,32) (19,5) (8,3) (18,21) (9,26) (30,9) (10,16) (11,12) (8,2) (17,33) (20,0) (31,30) (6,20) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph720",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,19) (28,0) (2,14) (16,2) (19,10) (24,3) (15,30) (12,27) (2,23) (24,17) (12,32) (18,24) (32,5) (8,5) (25,21) (27,31) (29,14) (20,27) (5,11) (11,9) (19,32) (26,32) (24,14) (1,5) (4,12) (29,0) (6,9) (16,25) (14,5) (22,13) (20,22) (30,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1940",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,28) (5,19) (16,33) (13,22) (9,2) (29,31) (0,23) (24,5) (7,21) (19,1) (7,23) (12,4) (6,9) (10,21) (26,17) (12,22) (27,20) (1,0) (14,34) (13,28) (0,17) (17,1) (32,31) (25,24) (32,4) (11,5) (18,34) (11,16) (12,30) (3,12) (27,26) (20,15) (6,17) (0,2) (30,18) (8,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1911",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,21) (20,18) (22,18) (9,10) (21,11) (13,32) (25,22) (28,1) (0,1) (4,13) (31,19) (2,0) (32,2) (16,1) (14,24) (12,30) (3,29) (27,22) (24,7) (14,28) (17,10) (33,15) (8,30) (11,19) (34,6) (34,18) (24,11) (28,15) (1,27) (9,28) (19,29) (4,8) (0,23) (26,14) (32,21) (0,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1738",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,7) (21,29) (2,11) (25,12) (17,26) (1,20) (30,24) (3,23) (25,13) (31,14) (29,23) (12,10) (0,2) (0,14) (31,5) (17,1) (5,25) (2,5) (32,6) (29,12) (8,18) (4,24) (31,22) (8,9) (16,7) (28,31) (13,19) (26,30) (32,15) (1,0) (1,14) (16,6) (27,24) (8,15) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1086",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,1) (10,9) (12,18) (3,25) (4,2) (4,15) (9,25) (17,16) (23,1) (3,13) (20,2) (2,0) (8,24) (7,16) (6,7) (11,17) (5,24) (3,5) (11,8) (9,21) (12,17) (14,23) (12,0) (15,19) (1,0) (22,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph685",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,13) (31,28) (3,24) (9,17) (7,24) (15,5) (6,11) (10,16) (9,18) (26,28) (10,1) (31,25) (31,21) (7,1) (27,19) (13,20) (4,23) (10,12) (5,16) (29,22) (19,4) (20,21) (13,8) (20,10) (0,28) (30,19) (2,23) (14,12) (18,0) (10,11) (5,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1297",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,22) (23,21) (27,6) (19,8) (11,9) (6,0) (0,1) (27,24) (21,18) (15,1) (26,5) (16,27) (8,1) (12,2) (1,9) (13,20) (24,17) (4,24) (27,26) (12,20) (18,9) (15,14) (26,7) (3,0) (23,26) (0,2) (3,25) (3,18) (3,13) (10,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1319",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,10) (23,10) (4,24) (16,27) (3,26) (18,23) (20,9) (26,7) (16,3) (0,2) (1,0) (17,16) (24,28) (28,14) (0,3) (9,26) (0,4) (20,19) (23,12) (3,12) (24,0) (0,5) (11,0) (26,13) (2,15) (22,2) (13,14) (25,27) (22,26) (21,23) (1,25) (6,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph896",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,16) (11,13) (26,1) (23,13) (17,12) (25,6) (2,30) (32,1) (23,32) (4,18) (8,12) (1,24) (9,1) (22,19) (28,17) (29,14) (22,3) (33,23) (31,11) (18,33) (27,15) (8,20) (6,5) (13,3) (27,29) (26,28) (2,23) (21,0) (7,5) (10,19) (5,31) (22,27) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1945",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (29,11) (27,20) (28,29) (6,2) (5,12) (14,34) (6,14) (24,9) (7,22) (26,8) (4,27) (14,30) (22,12) (22,10) (21,7) (9,32) (24,15) (3,20) (19,29) (7,26) (32,14) (34,17) (13,14) (14,31) (0,24) (23,0) (27,30) (1,12) (0,10) (25,4) (1,0) (28,30) (16,34) (33,8) (14,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph484",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,28) (11,22) (26,9) (17,2) (6,15) (8,9) (22,3) (16,20) (20,29) (19,28) (1,21) (13,9) (20,21) (25,14) (8,11) (1,4) (25,24) (26,27) (5,2) (10,18) (21,7) (0,6) (17,23) (15,8) (28,15) (23,4) (14,18) (2,11) (18,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph349",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,21) (28,1) (26,5) (14,25) (15,16) (28,17) (3,18) (6,18) (11,25) (9,17) (13,0) (5,15) (26,27) (22,24) (25,23) (8,13) (3,24) (25,8) (21,18) (16,4) (1,10) (19,21) (10,20) (17,7) (18,12) (2,18) (2,26) (25,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph73",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,0) (21,19) (24,7) (2,8) (23,22) (10,4) (12,0) (1,15) (8,15) (17,0) (18,25) (11,9) (7,17) (14,4) (13,12) (16,11) (6,21) (16,5) (22,19) (19,4) (3,21) (15,11) (14,20) (25,14) (8,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1139",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (5,19) (19,10) (0,1) (2,7) (1,8) (15,22) (25,11) (22,1) (13,23) (6,4) (13,22) (0,19) (0,2) (5,17) (10,25) (1,26) (16,3) (12,14) (20,18) (7,8) (0,9) (14,5) (21,23) (3,23) (7,4) (11,20) (17,21) (2,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1886",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,5) (24,15) (14,23) (19,30) (3,0) (21,32) (5,33) (15,16) (1,4) (11,19) (6,9) (1,0) (22,31) (0,26) (19,18) (26,13) (19,14) (17,18) (8,24) (24,26) (29,1) (15,6) (21,29) (28,21) (12,3) (14,21) (20,28) (5,15) (31,3) (12,10) (4,25) (23,2) (25,9) (29,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1554",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,26) (6,15) (26,14) (3,30) (29,25) (0,2) (10,5) (12,5) (30,6) (25,6) (14,20) (21,14) (19,24) (18,1) (11,25) (23,8) (25,17) (12,30) (14,13) (4,0) (0,1) (16,27) (27,15) (26,11) (9,21) (6,7) (18,23) (2,5) (3,0) (30,28) (7,8) (4,21) (14,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1493",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,11) (16,18) (26,8) (21,14) (17,20) (29,2) (22,1) (25,19) (15,26) (14,29) (6,19) (26,3) (14,13) (25,9) (19,27) (20,11) (23,13) (5,2) (23,10) (20,1) (23,12) (29,9) (3,21) (1,0) (19,4) (21,7) (16,24) (12,28) (25,16) (0,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1710",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,21) (25,23) (30,18) (28,24) (12,11) (30,2) (27,28) (7,9) (9,22) (30,12) (15,27) (16,19) (0,3) (28,20) (2,0) (32,7) (23,10) (29,4) (6,29) (0,12) (8,1) (21,3) (2,26) (4,0) (1,9) (0,1) (10,7) (17,15) (6,21) (3,5) (32,13) (0,27) (5,11) (22,31) (8,24) (14,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph944",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,21) (22,29) (2,5) (30,26) (30,24) (7,24) (26,33) (27,29) (4,6) (12,11) (24,9) (10,8) (32,15) (5,31) (17,33) (13,20) (14,0) (14,1) (23,3) (1,17) (5,25) (31,23) (4,34) (8,19) (12,25) (16,6) (7,16) (8,15) (18,2) (32,12) (31,14) (24,28) (25,13) (29,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1013",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,25) (10,16) (3,1) (4,14) (7,5) (24,14) (17,23) (14,20) (18,13) (4,25) (10,17) (2,0) (1,6) (17,15) (3,25) (25,12) (0,21) (1,0) (5,2) (13,19) (0,3) (2,19) (11,8) (21,13) (14,18) (11,25) (16,22) (10,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1731",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,19) (15,17) (0,12) (20,10) (32,12) (28,9) (1,32) (17,16) (26,9) (10,24) (28,7) (20,4) (20,17) (11,13) (28,14) (22,17) (2,8) (0,29) (7,5) (27,0) (19,7) (21,29) (18,11) (8,14) (30,32) (26,15) (28,23) (13,22) (27,16) (1,0) (31,2) (3,7) (32,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph27",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,16) (17,4) (25,2) (0,22) (18,11) (4,14) (16,9) (7,20) (18,15) (1,20) (5,12) (18,17) (4,0) (3,2) (23,2) (1,21) (0,1) (10,24) (6,1) (12,7) (16,13) (18,8) (20,10) (25,19) (9,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph819",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,25) (18,25) (18,32) (15,11) (30,4) (22,26) (23,3) (12,28) (26,6) (19,8) (17,22) (11,2) (31,2) (28,16) (24,23) (29,13) (16,21) (3,6) (13,30) (12,7) (20,18) (24,28) (0,27) (1,12) (2,9) (13,5) (11,19) (8,6) (15,33) (28,4) (18,19) (31,0) (12,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1858",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (1,27) (29,1) (0,3) (31,28) (15,31) (8,2) (23,17) (12,6) (11,13) (27,19) (20,6) (13,24) (33,1) (14,28) (30,0) (5,7) (8,28) (26,1) (4,16) (0,1) (4,3) (24,0) (1,20) (9,30) (24,18) (10,24) (16,1) (25,6) (22,28) (31,33) (2,0) (32,14) (17,14) (13,27) (7,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1636",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,29) (29,24) (29,1) (1,23) (8,12) (4,27) (31,18) (14,6) (19,9) (29,7) (20,22) (26,17) (10,30) (13,22) (17,16) (20,6) (11,2) (31,28) (1,0) (28,0) (31,21) (3,31) (4,0) (27,8) (30,2) (15,5) (2,0) (3,19) (0,3) (16,5) (9,12) (1,19) (24,25) (12,26) (22,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph635",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,25) (14,12) (8,18) (3,30) (25,7) (5,9) (2,16) (1,5) (19,13) (1,29) (26,1) (16,14) (28,25) (12,17) (27,5) (0,30) (28,23) (25,13) (4,11) (9,21) (1,15) (2,6) (24,12) (17,20) (8,31) (0,4) (26,22) (6,11) (5,12) (18,13) (7,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph476",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,17) (16,4) (18,9) (20,26) (22,1) (1,27) (7,14) (29,17) (12,27) (19,18) (11,18) (1,8) (28,13) (7,20) (25,10) (10,20) (2,25) (1,26) (25,21) (4,17) (5,2) (28,3) (28,29) (0,23) (0,4) (2,24) (0,26) (6,12) (15,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1890",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,19) (16,17) (12,33) (2,32) (0,1) (22,13) (28,24) (20,17) (2,8) (12,0) (10,20) (7,5) (18,11) (30,0) (21,29) (14,28) (31,32) (9,26) (29,32) (16,27) (14,8) (1,32) (4,20) (33,22) (0,27) (17,23) (13,11) (7,3) (15,17) (26,15) (25,10) (9,28) (7,19) (7,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1204",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,0) (11,19) (5,22) (17,26) (0,3) (19,15) (24,13) (4,14) (18,11) (12,27) (1,9) (16,13) (8,11) (14,3) (12,13) (25,20) (19,27) (0,1) (0,23) (18,25) (2,0) (2,1) (6,24) (15,22) (19,14) (17,24) (21,3) (21,9) (4,7) (22,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1716",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,9) (7,20) (8,18) (6,0) (27,8) (14,21) (24,30) (31,2) (6,31) (2,0) (18,1) (15,12) (11,29) (0,15) (16,29) (9,2) (21,23) (20,16) (27,12) (18,32) (0,5) (1,0) (31,4) (28,2) (8,14) (25,22) (23,17) (2,25) (12,10) (29,9) (3,2) (31,13) (30,18) (26,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1373",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,4) (0,3) (2,0) (5,11) (14,24) (15,23) (4,13) (18,11) (0,21) (28,5) (11,14) (1,15) (20,8) (21,19) (26,19) (12,16) (9,21) (0,17) (2,8) (22,25) (10,11) (0,12) (8,15) (20,25) (0,1) (6,16) (22,27) (17,7) (0,4) (7,27) (21,3) (19,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph533",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,23) (21,8) (22,3) (28,14) (16,4) (21,7) (4,10) (19,20) (15,30) (27,5) (29,18) (5,0) (4,3) (28,13) (20,27) (8,17) (1,28) (27,23) (24,11) (28,26) (13,0) (2,3) (25,18) (28,21) (18,30) (10,15) (13,2) (24,10) (25,9) (28,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph168",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,7) (26,5) (24,25) (24,21) (12,7) (5,19) (14,9) (16,10) (2,21) (4,14) (13,15) (20,17) (14,8) (22,3) (21,16) (3,10) (18,15) (5,25) (22,8) (20,15) (15,9) (8,6) (11,10) (5,0) (6,23) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1809",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (28,32) (9,30) (11,14) (21,14) (7,29) (23,9) (12,33) (7,27) (20,19) (26,23) (3,20) (17,33) (10,2) (30,29) (17,28) (25,30) (6,25) (4,29) (4,16) (4,0) (5,24) (1,0) (8,1) (22,21) (13,9) (2,15) (33,18) (3,1) (21,32) (8,18) (31,4) (5,25) (1,2) (27,14) (0,2) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1499",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,2) (12,24) (8,10) (5,12) (13,9) (7,15) (22,3) (20,18) (11,8) (29,18) (9,6) (26,19) (7,27) (10,17) (22,26) (7,5) (4,8) (29,23) (8,16) (2,6) (20,28) (1,0) (14,2) (0,20) (11,26) (26,15) (15,1) (2,26) (17,21) (25,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph767",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,20) (22,29) (21,7) (16,3) (18,22) (12,19) (18,32) (3,11) (32,17) (5,12) (26,1) (25,1) (1,7) (4,14) (31,4) (11,9) (15,25) (16,23) (24,26) (2,7) (5,29) (11,27) (17,0) (6,32) (26,22) (31,27) (10,29) (12,16) (30,8) (28,27) (13,19) (31,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph563",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,26) (17,12) (29,12) (6,18) (10,20) (22,28) (28,2) (5,26) (16,4) (30,27) (25,0) (23,1) (14,29) (10,29) (10,9) (5,13) (6,3) (27,0) (20,13) (10,11) (11,8) (21,24) (8,4) (10,19) (11,7) (15,21) (8,2) (22,1) (16,25) (0,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph36",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,11) (10,9) (14,24) (4,14) (2,19) (16,22) (25,4) (17,25) (17,23) (14,18) (25,12) (3,25) (1,6) (19,13) (14,20) (2,5) (1,3) (5,7) (11,8) (21,13) (17,15) (13,18) (16,10) (17,10) (0,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph121",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,6) (17,24) (3,21) (22,6) (20,5) (5,16) (6,2) (14,4) (15,1) (16,19) (10,19) (24,21) (0,23) (7,23) (6,26) (13,22) (17,11) (24,4) (19,21) (13,23) (15,18) (25,7) (1,12) (9,13) (13,20) (1,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph519",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,7) (23,16) (21,2) (5,24) (11,30) (12,26) (15,8) (6,20) (19,23) (14,21) (9,23) (25,12) (14,9) (3,8) (17,8) (27,28) (22,4) (19,1) (3,29) (21,27) (7,8) (7,13) (24,12) (16,10) (20,2) (28,30) (22,14) (18,9) (3,0) (29,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1337",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,12) (21,12) (20,0) (15,25) (8,12) (1,2) (11,5) (0,2) (15,23) (6,28) (3,7) (25,7) (18,15) (12,26) (0,3) (9,4) (7,4) (10,6) (14,12) (0,14) (1,13) (16,19) (1,0) (4,17) (6,16) (26,27) (28,2) (6,18) (22,20) (22,11) (24,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph20",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,9) (15,23) (6,20) (9,17) (14,20) (0,3) (21,2) (21,14) (22,9) (24,5) (25,7) (3,24) (23,12) (1,19) (24,12) (8,13) (10,16) (23,18) (21,12) (8,7) (3,8) (4,22) (8,16) (11,7) (2,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1055",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (15,9) (13,15) (6,20) (19,5) (14,4) (8,6) (24,25) (12,7) (0,5) (8,14) (18,15) (16,10) (22,3) (25,23) (22,8) (3,10) (6,7) (10,11) (16,21) (2,21) (5,15) (24,21) (9,14) (17,20) (3,1) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph763",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,22) (27,23) (14,17) (15,2) (19,28) (32,9) (19,25) (1,27) (20,21) (15,5) (1,16) (0,8) (11,22) (17,3) (7,30) (20,18) (7,3) (9,31) (20,3) (3,24) (28,6) (12,26) (29,26) (12,11) (11,25) (21,16) (10,7) (14,5) (11,16) (4,1) (11,8) (19,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph814",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,14) (14,21) (29,7) (28,32) (18,8) (25,30) (16,4) (22,21) (4,31) (20,3) (6,25) (33,12) (13,9) (18,33) (30,9) (17,28) (29,30) (0,4) (24,5) (1,2) (29,4) (3,1) (8,1) (23,26) (5,25) (2,15) (33,17) (14,27) (10,2) (19,20) (32,21) (7,27) (9,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph480",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,24) (6,23) (5,27) (8,2) (3,8) (24,16) (1,4) (3,15) (29,22) (10,2) (13,12) (19,13) (15,14) (15,0) (15,11) (4,18) (21,25) (28,25) (22,0) (0,24) (24,9) (12,26) (14,17) (26,27) (7,25) (3,6) (20,12) (20,18) (19,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph459",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,11) (6,19) (0,8) (22,12) (10,15) (3,12) (26,18) (13,20) (23,25) (21,28) (27,0) (15,9) (5,23) (20,3) (13,9) (0,24) (7,14) (29,28) (27,12) (17,10) (26,19) (1,2) (16,5) (12,11) (29,16) (20,28) (19,11) (4,18) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph376",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,18) (1,18) (6,15) (21,27) (3,13) (15,4) (23,8) (0,27) (22,25) (21,19) (12,16) (9,11) (19,1) (4,5) (11,12) (11,2) (28,3) (5,23) (2,14) (28,10) (26,11) (19,26) (3,12) (17,24) (7,18) (17,28) (25,3) (3,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph9",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,7) (16,1) (15,14) (6,17) (22,25) (9,12) (11,21) (5,7) (19,22) (16,17) (13,17) (18,21) (0,7) (20,10) (23,14) (8,7) (3,5) (24,8) (22,12) (17,23) (2,17) (16,20) (12,11) (12,8) (10,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph39",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,22) (20,17) (9,8) (2,15) (0,11) (8,0) (7,3) (10,14) (10,22) (12,24) (24,2) (10,21) (25,22) (18,20) (6,5) (16,15) (3,11) (23,4) (23,3) (16,19) (22,17) (4,1) (6,17) (13,24) (12,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph600",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,5) (7,15) (22,20) (19,6) (9,18) (21,25) (21,4) (12,24) (15,14) (21,17) (0,30) (3,23) (21,14) (14,20) (27,29) (27,26) (6,27) (30,8) (28,5) (16,5) (20,13) (4,5) (23,22) (12,4) (2,17) (17,27) (21,10) (22,9) (0,14) (31,1) (6,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1754",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,13) (14,19) (13,32) (8,14) (10,25) (29,12) (7,1) (25,1) (17,8) (22,9) (13,15) (7,5) (28,14) (28,21) (18,7) (3,0) (20,8) (26,24) (5,27) (0,5) (25,23) (13,26) (4,0) (11,9) (25,21) (2,3) (6,7) (30,0) (16,2) (30,21) (9,2) (15,23) (3,8) (0,2) (0,1) (13,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph128",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,7) (7,6) (9,3) (7,8) (18,13) (0,17) (19,16) (23,11) (0,19) (21,23) (2,25) (0,10) (3,21) (4,15) (1,13) (26,17) (16,7) (18,24) (17,22) (8,12) (2,6) (2,23) (1,0) (23,4) (3,20) (5,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph50",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,24) (8,22) (20,24) (4,19) (0,16) (0,9) (1,15) (18,15) (16,8) (7,1) (23,11) (14,25) (16,14) (21,23) (3,9) (10,6) (19,11) (2,23) (17,4) (13,10) (17,15) (21,12) (24,17) (14,6) (5,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph693",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (31,24) (0,17) (31,18) (11,5) (9,21) (29,16) (12,22) (12,4) (6,17) (27,20) (13,22) (19,1) (17,1) (5,19) (27,26) (30,12) (20,28) (28,13) (10,20) (12,3) (6,8) (2,9) (24,21) (5,23) (14,7) (15,0) (17,26) (30,18) (7,23) (11,16) (4,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1923",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,20) (32,13) (17,8) (16,33) (2,3) (34,6) (12,26) (7,19) (26,9) (11,2) (30,25) (21,24) (16,22) (2,19) (1,4) (5,19) (30,4) (6,20) (4,26) (3,9) (17,9) (13,27) (31,14) (0,1) (29,18) (21,1) (7,18) (0,2) (5,23) (0,7) (17,10) (20,11) (27,4) (8,31) (0,28) (16,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph525",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,25) (13,10) (10,28) (0,30) (26,8) (7,28) (15,3) (16,11) (12,6) (23,8) (27,30) (4,18) (2,21) (6,20) (14,16) (21,18) (4,19) (17,16) (24,10) (0,9) (28,9) (29,8) (5,1) (11,12) (26,3) (3,22) (8,19) (25,13) (9,16) (24,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1832",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,25) (7,18) (30,0) (21,14) (1,30) (16,8) (8,21) (28,22) (27,5) (14,33) (6,25) (15,11) (31,4) (12,10) (2,0) (32,9) (6,9) (30,16) (25,33) (26,27) (29,15) (24,11) (22,0) (3,26) (21,18) (16,19) (0,1) (17,2) (3,28) (4,13) (4,5) (16,17) (3,0) (31,15) (23,20) (12,4) (0,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph742",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (26,16) (10,19) (20,1) (24,29) (32,5) (0,25) (9,1) (2,4) (9,19) (5,18) (14,23) (13,24) (16,17) (18,4) (30,14) (11,3) (20,28) (7,23) (31,15) (23,29) (26,1) (22,6) (12,14) (0,28) (8,21) (32,22) (14,21) (15,22) (22,17) (11,8) (31,23) (27,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph325",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,12) (23,1) (0,20) (4,25) (23,18) (24,11) (3,27) (8,4) (2,19) (1,5) (6,14) (1,21) (27,5) (7,28) (28,1) (28,8) (19,14) (10,16) (23,14) (17,16) (11,16) (23,26) (15,13) (5,22) (9,6) (23,11) (27,0) (22,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph852",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,29) (19,13) (16,3) (30,16) (3,13) (6,25) (29,1) (10,7) (11,4) (33,7) (25,13) (10,24) (22,8) (14,21) (29,5) (20,7) (26,13) (9,11) (27,7) (14,19) (29,25) (5,28) (17,29) (18,32) (15,27) (23,26) (0,9) (22,23) (12,22) (31,21) (17,24) (32,11) (12,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1797",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (13,22) (8,7) (5,25) (0,27) (1,32) (9,14) (1,0) (16,6) (26,4) (22,11) (29,3) (9,15) (18,21) (17,25) (21,17) (3,20) (2,5) (5,30) (5,20) (29,10) (16,26) (21,8) (9,29) (30,26) (14,28) (19,13) (4,23) (2,0) (21,19) (24,10) (0,8) (12,4) (31,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph999",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,12) (30,13) (1,30) (7,33) (2,32) (8,13) (9,14) (2,0) (19,2) (34,11) (15,1) (27,10) (13,5) (27,14) (18,34) (32,7) (30,17) (24,28) (23,15) (29,34) (0,29) (26,25) (22,15) (32,20) (8,9) (31,34) (3,8) (12,26) (21,10) (24,23) (6,27) (4,12) (3,16) (18,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph746",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,9) (22,23) (32,5) (14,25) (30,32) (17,27) (16,20) (30,28) (7,27) (6,14) (28,13) (3,18) (16,2) (15,21) (24,2) (1,18) (19,4) (28,25) (7,16) (12,21) (0,26) (26,10) (8,22) (12,30) (23,29) (8,7) (10,8) (14,18) (14,23) (29,4) (14,31) (11,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1619",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (9,19) (14,6) (24,29) (31,21) (18,31) (7,29) (24,25) (22,17) (8,27) (1,29) (12,26) (17,16) (15,5) (16,5) (12,8) (9,12) (30,10) (31,3) (19,3) (11,2) (22,13) (0,28) (27,4) (17,26) (31,28) (22,20) (19,1) (29,10) (1,0) (23,1) (2,30) (20,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph534",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,19) (6,13) (15,13) (8,18) (23,19) (0,9) (7,11) (29,23) (21,10) (21,16) (26,28) (25,30) (9,5) (8,7) (0,14) (27,13) (14,12) (2,15) (20,22) (20,7) (25,0) (22,17) (1,11) (27,9) (15,3) (24,9) (7,0) (4,21) (30,4) (26,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1333",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,6) (6,0) (27,15) (27,25) (24,7) (7,20) (13,24) (3,5) (24,21) (22,21) (27,26) (10,14) (23,12) (19,18) (19,28) (7,17) (21,18) (1,22) (4,26) (3,10) (8,28) (11,16) (18,11) (9,6) (24,14) (12,17) (17,27) (1,0) (2,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1177",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,25) (8,2) (7,25) (13,12) (12,0) (11,26) (17,0) (11,16) (7,17) (8,15) (4,14) (2,0) (21,3) (19,22) (0,21) (3,0) (22,24) (4,19) (0,1) (21,6) (21,19) (9,11) (8,20) (11,14) (16,5) (4,10) (18,15) (23,14) (15,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1045",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,0) (25,6) (18,8) (6,18) (20,12) (1,0) (2,19) (10,20) (17,13) (16,14) (24,0) (5,15) (16,17) (2,0) (21,7) (13,22) (0,4) (3,7) (11,3) (18,24) (24,9) (2,10) (1,17) (22,6) (11,19) (15,9) (8,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph473",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,16) (18,13) (25,17) (17,10) (25,19) (10,8) (1,3) (1,4) (29,25) (14,18) (11,7) (10,16) (29,9) (12,27) (21,17) (29,11) (2,5) (17,28) (25,15) (14,26) (23,14) (3,25) (13,27) (20,27) (13,22) (21,0) (24,26) (19,2) (5,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph56",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,3) (1,13) (2,24) (7,6) (7,8) (17,22) (23,21) (4,15) (6,2) (0,1) (0,19) (12,8) (4,23) (3,9) (0,10) (20,5) (18,13) (16,19) (7,14) (20,3) (23,11) (17,2) (23,18) (7,16) (25,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1122",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,14) (6,26) (20,8) (6,15) (14,18) (6,25) (3,21) (7,8) (14,17) (18,1) (5,9) (26,19) (2,0) (24,25) (21,4) (11,25) (22,11) (1,0) (16,14) (13,23) (12,5) (14,26) (15,23) (19,21) (12,25) (7,6) (5,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1661",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,28) (8,2) (3,0) (31,2) (10,0) (26,23) (20,6) (1,0) (12,30) (22,12) (6,2) (7,16) (12,18) (19,26) (1,14) (6,28) (5,23) (25,5) (16,26) (13,20) (31,15) (31,4) (5,21) (1,17) (4,0) (12,17) (0,2) (21,27) (9,30) (0,9) (23,11) (6,18) (24,16) (27,29) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1931",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,23) (0,2) (27,29) (31,15) (28,9) (33,5) (18,20) (10,2) (30,6) (34,6) (21,19) (14,25) (14,5) (4,23) (10,22) (4,11) (6,8) (25,22) (26,3) (27,7) (24,0) (32,33) (26,31) (16,2) (0,15) (17,20) (24,23) (23,34) (12,29) (17,21) (30,19) (0,1) (33,27) (9,1) (9,30) (1,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1289",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,26) (18,3) (3,25) (7,26) (19,8) (0,10) (8,1) (24,27) (3,13) (9,18) (0,1) (18,21) (6,27) (9,1) (23,26) (16,27) (0,6) (0,3) (27,26) (17,24) (23,21) (9,11) (15,1) (2,12) (15,14) (12,20) (20,13) (24,4) (4,0) (2,0) (18,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph195",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,8) (13,0) (2,21) (18,9) (13,25) (15,14) (4,11) (7,20) (4,5) (9,3) (1,7) (24,0) (21,5) (7,8) (20,25) (9,6) (25,17) (26,23) (22,2) (19,25) (10,1) (14,10) (25,23) (4,12) (1,12) (18,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1536",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,23) (25,20) (4,30) (5,25) (3,18) (4,0) (16,26) (6,0) (7,2) (0,2) (18,19) (7,30) (1,0) (4,27) (9,1) (10,15) (26,22) (18,0) (13,12) (11,1) (26,14) (13,27) (16,15) (24,8) (30,28) (23,29) (3,0) (1,5) (10,2) (8,20) (17,15) (1,13) (21,15) (14,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph447",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (16,12) (7,16) (12,22) (18,19) (27,0) (8,1) (2,15) (16,6) (11,17) (8,25) (13,15) (5,14) (4,3) (2,18) (26,24) (8,13) (17,13) (11,28) (20,5) (14,6) (27,24) (18,9) (13,0) (16,23) (9,21) (14,3) (15,29) (10,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1357",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,27) (27,15) (5,3) (1,0) (2,0) (0,6) (19,28) (6,7) (24,7) (27,26) (14,10) (24,13) (11,16) (1,22) (21,22) (10,3) (7,17) (19,2) (12,23) (27,17) (11,18) (9,6) (18,19) (4,26) (21,24) (18,21) (7,20) (17,12) (14,24) (8,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph962",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,20) (31,7) (8,0) (3,33) (19,25) (24,27) (34,17) (23,11) (11,8) (3,18) (14,5) (29,19) (20,3) (25,11) (5,15) (6,28) (16,1) (21,16) (1,28) (20,21) (22,13) (33,7) (12,11) (16,11) (4,1) (19,32) (3,27) (17,9) (2,15) (7,10) (26,30) (32,9) (26,12) (14,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1787",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,25) (25,8) (20,13) (31,15) (22,17) (4,19) (18,31) (1,14) (24,10) (32,0) (25,4) (2,31) (11,5) (6,13) (23,21) (16,22) (9,27) (21,28) (26,0) (20,32) (29,5) (9,8) (1,30) (27,1) (0,1) (7,20) (29,22) (11,21) (20,28) (12,18) (2,0) (3,11) (21,10) (21,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1386",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,9) (7,16) (11,12) (27,9) (1,25) (10,28) (22,8) (11,16) (16,15) (28,5) (19,8) (20,18) (24,10) (23,13) (9,28) (24,3) (3,21) (6,17) (1,2) (0,21) (8,25) (3,26) (1,0) (14,3) (6,12) (4,18) (10,13) (8,26) (4,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1764",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,2) (3,24) (12,4) (16,2) (30,3) (29,0) (13,22) (6,9) (24,14) (5,8) (11,5) (15,30) (19,32) (11,9) (2,14) (22,20) (17,24) (0,1) (2,0) (25,16) (10,19) (27,20) (5,32) (12,32) (3,0) (26,32) (31,27) (12,27) (25,21) (24,18) (1,5) (28,0) (5,14) (19,7) (14,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph235",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,22) (3,8) (26,5) (9,25) (2,4) (21,9) (5,24) (23,14) (9,10) (16,17) (25,24) (17,11) (23,1) (27,8) (18,12) (12,17) (0,12) (13,3) (15,19) (11,8) (7,16) (2,20) (6,7) (2,0) (4,15) (1,7) (3,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1516",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,2) (30,1) (16,21) (22,1) (10,26) (7,29) (22,19) (20,26) (13,0) (0,2) (24,29) (14,17) (15,20) (4,9) (10,25) (17,28) (13,28) (14,16) (9,27) (14,12) (7,2) (6,20) (6,8) (17,23) (19,15) (0,1) (18,14) (13,27) (3,9) (3,0) (8,14) (11,7) (5,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph500",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (21,7) (12,28) (1,15) (18,10) (6,23) (15,9) (10,22) (28,11) (12,20) (13,30) (19,2) (14,7) (4,14) (17,5) (1,6) (14,19) (28,6) (12,24) (23,29) (25,15) (28,27) (15,16) (25,17) (17,14) (8,9) (3,4) (29,26) (23,18) (30,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1579",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,23) (11,23) (29,25) (22,17) (28,7) (5,1) (8,4) (27,3) (28,8) (1,24) (27,0) (5,30) (27,11) (21,0) (14,6) (28,23) (23,19) (13,15) (10,16) (18,16) (23,14) (29,22) (29,4) (26,5) (20,14) (6,9) (0,1) (15,29) (22,12) (16,11) (2,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph155",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,20) (5,6) (14,10) (9,4) (14,0) (4,2) (8,14) (3,5) (20,22) (25,19) (19,23) (25,18) (14,3) (2,17) (21,16) (14,9) (7,24) (17,25) (24,5) (1,17) (20,15) (13,6) (11,16) (22,25) (16,15) (18,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1360",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (11,18) (9,23) (1,27) (14,11) (14,12) (0,7) (11,5) (27,15) (26,20) (15,16) (3,8) (1,21) (2,28) (19,13) (17,1) (5,4) (17,12) (23,25) (20,0) (0,1) (28,8) (24,13) (10,16) (2,7) (4,22) (6,1) (25,5) (26,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph957",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,27) (5,25) (20,19) (28,32) (18,33) (22,21) (33,12) (34,15) (3,20) (10,2) (4,31) (0,4) (25,6) (32,21) (3,1) (8,1) (27,7) (23,9) (29,34) (30,25) (11,14) (5,24) (28,34) (7,33) (18,8) (17,4) (9,13) (4,29) (2,1) (30,29) (21,14) (2,16) (26,23) (30,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1473",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (22,24) (13,22) (19,16) (21,23) (9,11) (23,6) (3,0) (2,1) (21,19) (0,4) (5,11) (12,28) (26,22) (19,4) (4,20) (25,22) (0,20) (17,11) (2,25) (14,7) (15,17) (7,25) (23,9) (29,14) (10,7) (19,3) (0,22) (1,0) (12,4) (27,10) (22,18) (2,0) (5,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1272",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,5) (17,10) (3,14) (20,16) (8,9) (5,4) (1,25) (0,1) (8,4) (23,1) (17,19) (0,2) (22,19) (0,4) (22,14) (14,16) (10,0) (6,19) (27,11) (13,23) (24,2) (7,11) (23,14) (21,15) (22,5) (0,18) (27,13) (21,19) (26,12) (10,2) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph49",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,25) (13,5) (14,6) (11,3) (2,24) (0,14) (18,21) (8,15) (22,8) (9,24) (10,2) (7,1) (20,11) (8,24) (13,21) (10,21) (15,16) (18,4) (15,23) (12,16) (21,17) (22,19) (21,14) (22,3) (23,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph165",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,21) (9,10) (26,22) (2,26) (23,11) (0,10) (10,6) (9,21) (16,12) (18,5) (20,24) (15,26) (17,0) (19,24) (25,23) (14,3) (7,11) (17,8) (26,21) (13,17) (19,0) (7,9) (4,14) (4,5) (12,15) (1,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1164",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,20) (10,8) (23,25) (3,14) (0,14) (5,9) (14,12) (16,2) (9,6) (26,2) (1,0) (19,1) (21,11) (4,26) (7,21) (18,6) (24,20) (4,0) (4,21) (26,9) (22,2) (7,1) (15,8) (2,0) (15,2) (2,13) (23,12) (23,19) (0,3) (21,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph792",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,22) (17,20) (8,18) (28,11) (13,26) (0,7) (7,28) (29,10) (13,9) (16,1) (24,17) (20,14) (28,16) (15,26) (25,4) (7,31) (3,18) (32,31) (27,20) (24,28) (21,9) (4,32) (5,2) (6,29) (22,18) (12,8) (1,8) (31,2) (6,5) (6,19) (24,23) (25,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1700",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,21) (7,21) (30,5) (27,12) (1,28) (31,15) (8,26) (4,13) (19,9) (32,1) (16,1) (7,2) (23,25) (0,8) (0,31) (2,17) (6,19) (3,30) (0,23) (28,10) (21,5) (13,9) (18,12) (24,3) (29,18) (0,1) (20,6) (31,2) (11,4) (20,32) (28,12) (15,14) (7,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph674",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,2) (6,12) (24,22) (15,11) (23,11) (18,29) (6,4) (25,14) (26,21) (23,28) (29,30) (11,26) (9,31) (27,11) (21,25) (16,12) (5,19) (12,1) (19,24) (30,17) (9,18) (2,9) (20,0) (8,27) (12,9) (7,16) (13,3) (22,27) (13,6) (15,0) (3,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1151",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,8) (14,26) (1,0) (0,23) (6,19) (22,24) (4,26) (16,22) (3,10) (8,2) (2,6) (25,9) (26,0) (25,14) (16,6) (12,8) (15,24) (20,16) (19,7) (17,6) (21,1) (16,5) (19,1) (10,0) (26,11) (13,4) (11,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph543",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,0) (29,25) (2,17) (24,26) (1,22) (22,2) (14,29) (4,19) (22,9) (20,3) (28,14) (5,13) (30,0) (4,25) (22,21) (26,8) (7,12) (0,24) (21,16) (23,20) (23,9) (27,14) (23,27) (24,18) (15,6) (12,6) (5,21) (5,6) (18,10) (5,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1972",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,2) (20,21) (1,7) (27,7) (1,0) (28,1) (18,33) (34,3) (0,30) (6,10) (16,2) (0,5) (10,30) (12,33) (16,13) (16,31) (11,32) (22,19) (17,24) (28,23) (25,17) (9,14) (0,25) (29,15) (5,32) (12,1) (0,3) (23,19) (34,29) (14,25) (4,15) (28,10) (26,24) (0,2) (11,22) (0,4) (21,23) (15,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1505",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,8) (25,9) (0,26) (16,22) (13,4) (6,16) (4,11) (7,19) (16,11) (0,25) (29,28) (5,16) (21,16) (8,12) (29,26) (15,26) (14,26) (4,24) (2,0) (8,20) (6,2) (19,6) (24,17) (10,3) (23,1) (1,19) (0,10) (0,1) (24,14) (30,11) (27,22) (18,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph256",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,19) (2,6) (0,1) (25,1) (7,27) (23,13) (24,3) (11,7) (18,21) (22,11) (10,14) (8,11) (21,11) (3,10) (7,5) (17,0) (27,4) (12,8) (5,16) (12,26) (7,23) (14,22) (1,15) (20,22) (9,16) (6,0) (8,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1362",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,13) (2,4) (3,14) (24,10) (2,0) (12,14) (21,27) (27,28) (14,9) (17,25) (23,25) (27,1) (28,25) (6,5) (5,26) (16,15) (2,17) (20,15) (1,0) (24,16) (17,7) (18,22) (25,19) (14,0) (20,19) (9,4) (14,11) (18,6) (5,3) (8,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph492",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,23) (13,0) (16,4) (20,6) (6,8) (19,22) (16,14) (14,11) (10,26) (29,22) (9,3) (12,14) (18,16) (7,27) (17,21) (2,28) (1,9) (13,26) (24,10) (14,17) (14,8) (25,20) (28,13) (7,2) (15,19) (5,27) (15,20) (7,9) (17,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph839",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,1) (11,18) (20,11) (17,13) (2,15) (31,0) (10,28) (7,8) (29,33) (12,13) (29,4) (20,30) (26,3) (11,24) (14,28) (23,5) (21,19) (19,12) (24,8) (27,14) (32,22) (9,22) (25,9) (6,5) (2,1) (19,26) (3,5) (30,12) (30,29) (10,2) (22,24) (16,3) (31,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1132",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,5) (21,13) (10,0) (13,14) (11,0) (26,13) (12,16) (0,17) (9,20) (0,1) (10,21) (10,25) (14,5) (2,0) (0,3) (3,7) (24,15) (18,21) (22,4) (5,19) (22,16) (1,12) (19,4) (7,24) (23,4) (6,10) (22,3) (14,20) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1470",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,9) (27,2) (2,26) (12,16) (27,7) (24,5) (14,4) (6,15) (18,1) (29,22) (20,22) (4,11) (13,1) (27,3) (8,14) (21,6) (13,4) (12,1) (0,15) (5,9) (25,20) (2,10) (1,0) (25,15) (9,17) (20,19) (28,6) (1,26) (17,25) (23,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph343",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,15) (9,21) (2,14) (26,0) (26,14) (21,24) (16,10) (16,0) (23,24) (6,28) (6,18) (22,11) (4,1) (1,12) (14,25) (16,28) (19,4) (5,28) (27,23) (23,4) (11,8) (17,21) (9,7) (3,18) (20,1) (28,8) (6,20) (7,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph668",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,21) (16,29) (18,8) (15,0) (18,1) (2,25) (12,15) (2,26) (30,6) (2,31) (29,11) (24,30) (2,9) (0,5) (2,3) (29,18) (4,31) (14,8) (20,7) (27,12) (19,9) (21,14) (16,20) (25,22) (12,10) (8,27) (18,31) (6,0) (28,9) (13,31) (17,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1987",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,6) (28,31) (28,8) (28,14) (33,14) (21,0) (19,27) (25,6) (26,1) (32,0) (24,18) (13,24) (16,1) (27,1) (3,4) (6,12) (15,31) (7,5) (11,13) (20,1) (17,14) (4,16) (1,0) (7,31) (23,17) (24,10) (0,24) (28,22) (13,27) (29,1) (1,33) (30,34) (8,2) (9,30) (31,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1995",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (25,0) (18,30) (12,6) (3,0) (34,16) (23,15) (24,11) (12,34) (4,5) (26,11) (2,16) (18,22) (1,17) (33,4) (10,12) (14,13) (12,27) (9,32) (20,3) (14,12) (17,0) (7,19) (0,4) (1,31) (24,29) (7,20) (12,5) (21,11) (21,20) (32,28) (31,16) (2,0) (0,1) (5,7) (32,30) (15,9) (8,15) (30,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1904",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (32,27) (30,20) (8,23) (23,1) (0,2) (15,16) (22,4) (18,14) (3,19) (5,27) (7,24) (0,13) (28,12) (11,17) (32,7) (31,6) (8,21) (13,29) (20,13) (2,4) (34,19) (15,9) (24,8) (6,16) (29,11) (30,19) (0,1) (1,28) (33,18) (29,33) (4,23) (25,10) (26,29) (10,26) (33,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph202",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,6) (1,16) (23,11) (26,24) (24,22) (14,3) (19,0) (5,18) (4,21) (27,4) (11,7) (15,26) (15,12) (16,12) (2,26) (23,26) (14,21) (19,25) (20,14) (10,9) (9,7) (13,17) (5,4) (17,8) (0,10) (17,0) (9,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph607",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (12,15) (11,24) (0,13) (4,8) (26,28) (0,29) (3,14) (5,22) (10,3) (30,13) (24,20) (7,16) (13,31) (0,8) (7,23) (29,1) (15,6) (28,8) (27,8) (16,2) (17,11) (30,18) (19,15) (23,26) (25,17) (22,13) (21,6) (4,10) (10,24) (0,15) (9,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph392",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,16) (14,28) (9,5) (22,15) (11,4) (26,7) (24,18) (4,23) (12,16) (0,27) (28,10) (8,14) (12,13) (2,3) (24,1) (15,28) (25,0) (6,8) (17,26) (0,3) (20,2) (2,22) (18,9) (21,0) (19,7) (13,9) (19,14) (23,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph501",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,30) (21,15) (2,7) (3,18) (1,5) (15,16) (13,12) (2,10) (9,1) (20,25) (26,16) (13,1) (18,0) (4,30) (15,17) (29,23) (27,13) (22,26) (5,25) (19,18) (1,11) (26,14) (30,28) (6,14) (23,11) (20,8) (15,10) (27,4) (8,24) (0,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph93",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,10) (24,15) (9,19) (4,7) (12,0) (2,19) (17,2) (12,20) (4,24) (22,17) (21,16) (1,12) (23,13) (15,6) (18,8) (19,25) (21,22) (7,5) (6,3) (6,13) (12,16) (2,14) (11,7) (8,23) (19,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1489",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,26) (10,29) (9,19) (13,18) (15,29) (20,16) (7,5) (25,6) (16,0) (11,27) (20,13) (21,2) (10,3) (0,2) (11,17) (7,8) (4,1) (22,0) (28,8) (24,5) (25,23) (20,23) (3,0) (17,8) (29,12) (28,9) (17,2) (14,25) (1,0) (2,18) (13,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph992",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,8) (22,3) (1,20) (18,5) (31,23) (29,19) (32,25) (11,25) (17,6) (23,27) (32,16) (27,33) (10,19) (12,24) (26,18) (18,30) (34,12) (21,13) (29,30) (20,0) (0,7) (0,13) (14,24) (3,11) (28,5) (32,4) (2,1) (30,8) (6,15) (6,26) (5,25) (13,23) (4,9) (27,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1254",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (9,1) (0,6) (18,21) (2,12) (5,26) (15,14) (1,8) (9,18) (16,27) (18,3) (24,4) (25,3) (0,10) (18,22) (19,8) (26,23) (9,11) (1,15) (17,24) (27,24) (0,1) (27,6) (21,23) (26,27) (26,7) (13,3) (20,12) (20,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph293",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,5) (23,20) (11,6) (6,13) (19,22) (21,5) (14,0) (3,12) (15,21) (16,2) (20,27) (27,14) (5,12) (4,18) (26,23) (21,9) (5,10) (26,7) (18,8) (22,1) (25,4) (24,17) (22,24) (9,23) (24,0) (2,22) (14,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1973",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (34,32) (7,6) (33,13) (18,19) (1,13) (31,11) (1,0) (12,10) (22,4) (29,23) (15,30) (20,9) (14,33) (6,16) (3,27) (25,8) (5,21) (24,32) (23,5) (15,0) (5,9) (28,34) (14,3) (12,17) (23,18) (25,26) (30,17) (19,2) (18,25) (1,16) (16,17) (6,11) (4,1) (10,19) (21,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph930",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,2) (34,13) (13,17) (23,5) (3,15) (11,19) (14,26) (21,25) (8,16) (7,8) (29,1) (24,4) (10,31) (13,18) (28,30) (6,24) (32,20) (32,4) (17,12) (10,15) (7,3) (21,2) (6,18) (27,10) (11,0) (8,32) (28,27) (23,9) (26,5) (29,22) (21,0) (29,10) (5,17) (14,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1417",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,2) (21,29) (7,9) (8,1) (13,11) (16,25) (18,24) (26,9) (24,11) (4,14) (23,2) (14,23) (22,5) (1,0) (10,7) (15,14) (12,22) (28,20) (0,3) (19,5) (6,10) (23,12) (25,3) (14,8) (29,26) (17,3) (20,6) (13,16) (17,27) (21,1) (0,4) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph395",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,13) (17,2) (8,17) (28,9) (23,20) (2,18) (5,22) (20,13) (26,15) (27,8) (11,25) (7,8) (1,0) (3,10) (19,2) (14,9) (21,0) (13,18) (25,6) (12,15) (4,1) (16,20) (5,7) (11,17) (12,28) (0,16) (25,10) (24,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1983",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,9) (23,34) (6,11) (26,2) (17,30) (27,1) (7,17) (22,27) (29,10) (12,27) (1,0) (8,5) (26,29) (3,0) (34,25) (4,23) (32,29) (31,0) (30,19) (4,17) (1,28) (22,33) (19,11) (19,5) (0,27) (13,2) (4,0) (15,31) (8,16) (19,20) (23,18) (0,2) (21,27) (10,16) (14,1) (22,13) (3,34) (24,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph491",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,15) (14,26) (13,27) (10,15) (14,6) (28,16) (20,25) (12,13) (5,1) (3,18) (18,21) (25,5) (11,23) (23,7) (4,19) (6,0) (0,18) (20,8) (4,27) (10,2) (17,15) (8,26) (15,22) (26,24) (19,29) (13,1) (2,7) (1,9) (11,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph972",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,27) (27,12) (7,19) (3,8) (13,29) (32,11) (14,13) (4,8) (15,6) (16,12) (23,31) (31,10) (8,10) (28,9) (14,24) (4,1) (21,18) (9,30) (5,34) (10,19) (32,26) (31,32) (21,33) (21,6) (18,3) (30,27) (6,22) (20,9) (13,1) (2,8) (0,20) (15,17) (34,17) (25,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1290",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,2) (9,11) (9,5) (1,13) (27,25) (23,2) (25,17) (6,21) (1,18) (17,9) (1,12) (16,12) (25,15) (4,14) (19,20) (20,6) (10,2) (0,15) (4,11) (0,1) (8,14) (22,5) (7,27) (3,27) (13,4) (6,15) (6,26) (1,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1227",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,6) (22,25) (3,10) (27,20) (2,0) (23,5) (18,7) (0,1) (15,12) (3,16) (24,17) (0,4) (12,3) (11,26) (19,26) (23,8) (17,3) (11,12) (0,3) (21,25) (4,5) (18,5) (11,2) (4,14) (20,3) (18,1) (2,13) (19,21) (9,11) (27,0) (1,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1613",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,0) (0,3) (13,12) (3,8) (14,28) (23,25) (7,5) (8,14) (0,30) (12,29) (15,13) (26,13) (21,30) (0,1) (28,21) (27,5) (25,21) (9,2) (18,7) (31,13) (10,25) (19,14) (23,15) (11,9) (1,7) (8,17) (7,6) (22,9) (2,0) (3,2) (25,1) (26,24) (2,16) (20,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1321",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,3) (18,21) (3,18) (5,26) (26,2) (11,25) (20,21) (1,0) (23,25) (13,0) (25,14) (2,18) (16,25) (8,13) (25,8) (26,27) (18,12) (21,19) (18,6) (20,10) (4,16) (15,16) (17,7) (28,1) (17,28) (17,9) (1,10) (24,22) (5,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1296",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,21) (15,20) (26,19) (20,1) (19,4) (5,2) (8,23) (23,12) (22,16) (2,19) (26,10) (25,9) (7,26) (14,27) (17,16) (0,1) (16,25) (14,21) (21,6) (19,25) (11,14) (12,9) (13,14) (3,21) (20,11) (3,24) (13,23) (18,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph261",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,12) (7,11) (8,4) (13,23) (23,1) (17,19) (0,10) (22,14) (4,5) (6,19) (12,5) (8,9) (20,16) (2,10) (2,24) (22,5) (1,25) (10,17) (16,14) (23,14) (22,19) (3,14) (18,0) (21,19) (27,13) (27,11) (15,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1794",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (14,10) (25,30) (5,3) (31,15) (16,31) (1,20) (28,8) (2,30) (9,4) (12,7) (24,6) (2,0) (15,17) (29,21) (26,11) (2,21) (28,16) (5,23) (0,9) (22,4) (10,15) (24,27) (6,32) (11,19) (19,22) (3,0) (3,29) (9,18) (1,12) (0,1) (5,31) (6,29) (31,7) (13,22) (26,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1598",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,6) (0,16) (29,15) (30,26) (17,20) (18,3) (8,0) (2,8) (2,0) (21,16) (10,11) (6,13) (5,25) (0,1) (4,17) (21,20) (30,25) (22,30) (30,14) (28,27) (19,7) (0,26) (19,24) (10,6) (9,3) (23,17) (27,8) (7,12) (7,4) (5,15) (15,9) (25,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph444",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,6) (0,17) (20,3) (0,1) (24,17) (19,16) (21,23) (3,9) (16,7) (27,2) (28,23) (0,10) (0,19) (26,18) (8,12) (5,20) (7,8) (13,1) (13,18) (23,11) (7,28) (7,14) (21,3) (22,29) (4,15) (25,2) (6,17) (4,23) (6,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph582",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,10) (17,10) (28,20) (0,15) (12,5) (14,3) (11,7) (14,16) (23,30) (24,2) (14,28) (5,4) (29,23) (9,8) (30,14) (0,10) (22,5) (25,19) (12,27) (19,21) (27,11) (30,22) (16,18) (21,13) (6,19) (19,22) (23,1) (26,1) (29,17) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph488",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (12,29) (16,20) (0,1) (9,19) (6,25) (23,20) (9,28) (18,2) (26,13) (27,11) (17,2) (25,14) (10,3) (4,1) (10,29) (2,21) (18,13) (8,28) (15,29) (20,13) (7,8) (7,5) (24,5) (11,17) (15,26) (23,25) (17,8) (0,16) (0,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1634",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,20) (28,6) (26,28) (13,1) (7,5) (28,23) (18,4) (22,16) (14,15) (22,12) (29,12) (14,17) (27,25) (21,26) (24,10) (22,8) (5,31) (31,30) (14,10) (0,1) (30,26) (3,22) (1,2) (18,5) (0,4) (14,26) (19,27) (6,2) (12,27) (19,17) (25,9) (11,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1358",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,14) (12,6) (12,28) (23,19) (25,11) (27,25) (1,18) (21,4) (7,6) (6,15) (15,26) (25,6) (0,1) (12,5) (9,5) (5,2) (23,17) (20,14) (26,14) (0,2) (16,25) (8,7) (8,22) (19,26) (3,21) (10,14) (3,0) (14,21) (24,11) (13,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1241",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,16) (22,10) (13,23) (20,7) (21,26) (21,3) (17,8) (12,9) (17,27) (4,25) (19,22) (17,11) (5,13) (24,16) (15,20) (0,3) (1,10) (15,3) (18,6) (25,27) (0,2) (6,7) (25,9) (2,4) (17,0) (0,1) (4,5) (24,22) (6,24) (17,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1555",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (14,23) (15,8) (21,18) (14,28) (8,29) (27,24) (26,1) (3,17) (4,5) (13,17) (19,29) (30,12) (22,23) (9,7) (22,17) (0,2) (7,5) (10,18) (8,12) (10,20) (0,7) (11,21) (2,16) (7,26) (16,20) (1,0) (6,26) (12,11) (27,30) (17,16) (25,12) (17,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph241",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,23) (8,12) (2,23) (3,21) (2,25) (6,17) (19,0) (2,6) (7,8) (4,15) (1,13) (1,0) (27,6) (4,23) (20,3) (17,22) (24,18) (3,9) (11,23) (18,13) (16,7) (16,19) (17,0) (7,14) (20,5) (0,10) (7,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1307",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,28) (10,6) (8,17) (14,3) (18,5) (5,4) (11,23) (1,0) (10,26) (26,15) (15,12) (19,25) (7,11) (27,23) (0,2) (9,21) (10,9) (16,1) (13,17) (26,2) (4,21) (12,16) (7,9) (28,0) (24,22) (14,21) (19,0) (26,24) (17,0) (14,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph929",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,16) (13,16) (23,19) (29,18) (21,24) (21,9) (14,18) (25,19) (20,0) (26,12) (23,2) (34,5) (29,33) (26,5) (28,10) (15,14) (1,29) (28,14) (27,1) (17,15) (31,1) (30,4) (1,9) (14,19) (18,0) (16,26) (14,8) (3,30) (18,6) (7,26) (22,19) (11,0) (23,16) (32,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph648",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,27) (13,31) (5,20) (10,2) (28,6) (5,0) (13,17) (25,3) (11,21) (10,15) (5,25) (31,15) (12,23) (23,13) (19,24) (24,22) (18,24) (1,11) (16,13) (28,5) (28,22) (29,7) (21,30) (4,29) (24,23) (27,29) (14,12) (19,26) (24,11) (29,8) (16,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph233",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,1) (21,3) (11,13) (20,1) (5,23) (15,13) (3,5) (20,6) (26,21) (24,9) (22,21) (13,17) (16,19) (18,19) (12,8) (15,27) (19,8) (9,1) (6,8) (24,4) (25,14) (15,3) (5,14) (3,2) (10,14) (0,2) (7,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1381",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,20) (7,9) (14,8) (3,17) (0,5) (1,21) (26,28) (3,2) (20,21) (14,23) (13,11) (13,16) (6,10) (2,23) (16,25) (3,25) (12,23) (4,0) (18,24) (5,22) (3,0) (26,9) (22,12) (8,1) (5,19) (0,2) (14,4) (27,17) (7,10) (1,0) (15,14) (24,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1099",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,17) (2,19) (12,24) (15,23) (7,25) (19,1) (7,8) (24,5) (21,14) (22,4) (0,4) (18,23) (3,0) (9,22) (14,9) (0,1) (24,3) (0,5) (13,8) (2,0) (23,12) (6,20) (20,14) (2,21) (21,12) (16,8) (16,10) (8,3) (7,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1369",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,5) (13,10) (12,2) (8,28) (18,28) (1,8) (9,22) (20,12) (23,15) (26,21) (9,4) (12,25) (24,3) (28,7) (9,27) (19,3) (1,13) (25,19) (1,0) (26,6) (18,11) (15,17) (16,14) (15,11) (24,4) (16,4) (25,8) (27,0) (16,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1007",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,7) (3,20) (8,20) (5,17) (2,20) (9,2) (9,13) (12,16) (16,23) (9,14) (18,19) (24,21) (1,5) (21,20) (22,10) (11,17) (16,19) (8,6) (0,18) (14,15) (20,5) (25,13) (21,10) (15,16) (0,1) (7,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph479",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,23) (24,29) (16,1) (26,16) (17,7) (5,11) (9,10) (9,13) (28,4) (14,0) (12,22) (21,28) (3,8) (0,19) (11,8) (3,27) (24,4) (18,6) (24,0) (13,2) (25,18) (0,20) (15,26) (19,11) (16,18) (28,7) (11,12) (10,3) (4,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph950",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,0) (11,25) (5,18) (22,15) (2,20) (21,31) (18,29) (30,4) (30,14) (25,13) (34,18) (10,3) (7,2) (32,4) (11,9) (7,24) (22,23) (23,25) (13,30) (6,10) (17,7) (5,33) (9,16) (4,3) (18,28) (26,14) (7,4) (6,5) (10,27) (22,1) (5,12) (8,7) (10,19) (13,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph441",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (24,13) (27,17) (9,11) (22,6) (5,12) (18,26) (1,9) (25,21) (22,3) (25,0) (12,13) (16,13) (22,20) (19,14) (24,28) (8,4) (24,7) (28,17) (10,21) (14,3) (15,23) (19,15) (14,4) (2,1) (27,19) (18,11) (11,19) (0,16) (5,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph333",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,8) (4,24) (17,27) (0,6) (1,15) (24,19) (3,13) (5,26) (15,16) (12,2) (9,12) (13,22) (1,9) (1,8) (6,26) (14,20) (7,26) (3,27) (9,18) (18,3) (26,23) (27,25) (0,10) (27,11) (21,18) (24,18) (23,21) (28,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph842",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,27) (7,31) (5,32) (26,9) (4,21) (19,6) (27,22) (13,15) (21,30) (17,32) (8,18) (20,13) (0,24) (22,6) (28,33) (14,22) (9,19) (29,4) (16,32) (2,16) (12,30) (6,31) (19,11) (30,13) (23,8) (25,10) (16,33) (6,8) (18,24) (25,16) (1,26) (3,2) (30,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1688",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,25) (0,3) (14,28) (28,17) (25,22) (29,13) (13,6) (15,20) (23,31) (20,7) (10,2) (2,0) (28,12) (9,19) (9,12) (0,4) (4,16) (19,13) (9,20) (18,9) (26,27) (23,16) (27,11) (26,21) (26,8) (18,26) (24,6) (1,6) (4,3) (29,10) (22,5) (6,30) (24,4) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1596",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (21,27) (2,0) (7,25) (8,9) (23,30) (25,19) (29,10) (7,12) (23,3) (1,0) (24,29) (8,27) (13,6) (14,16) (27,26) (9,18) (11,23) (25,28) (22,25) (4,29) (5,14) (20,17) (22,2) (5,15) (3,17) (13,14) (16,4) (11,22) (1,9) (26,15) (2,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph688",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,14) (12,10) (30,22) (5,17) (9,7) (4,13) (7,25) (26,2) (10,19) (11,10) (30,6) (30,11) (4,28) (8,6) (26,0) (21,15) (14,29) (23,26) (14,31) (16,3) (4,27) (10,1) (24,10) (21,26) (20,10) (1,18) (17,2) (27,23) (17,10) (3,2) (29,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph494",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,2) (24,27) (9,26) (6,19) (20,13) (21,18) (8,9) (12,25) (1,18) (27,0) (17,25) (8,19) (20,12) (27,16) (28,6) (29,16) (27,23) (13,5) (23,15) (10,2) (11,2) (26,11) (27,3) (5,14) (21,5) (4,1) (21,22) (23,25) (1,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph448",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,18) (13,8) (28,24) (24,29) (8,20) (18,29) (16,24) (25,11) (17,0) (2,10) (21,29) (27,18) (24,3) (29,22) (11,20) (10,27) (27,19) (1,23) (25,23) (9,13) (25,22) (23,6) (4,12) (7,10) (16,17) (9,4) (8,26) (4,5) (15,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph506",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,17) (22,20) (30,18) (14,13) (22,2) (23,21) (0,11) (16,19) (27,16) (10,23) (4,24) (9,26) (13,26) (1,25) (8,10) (12,25) (26,23) (26,7) (3,26) (23,24) (27,28) (3,16) (2,17) (29,28) (5,0) (0,18) (3,12) (9,20) (0,14) (15,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1111",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,17) (13,5) (14,23) (8,4) (16,17) (24,22) (1,21) (6,3) (13,25) (24,23) (16,7) (3,0) (23,1) (0,4) (25,8) (7,19) (1,20) (10,24) (14,4) (1,0) (16,12) (26,9) (18,21) (1,15) (20,17) (2,0) (2,11) (9,19) (3,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1263",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (9,23) (22,10) (24,7) (5,21) (16,22) (17,14) (13,3) (8,22) (6,13) (3,0) (11,14) (18,11) (1,0) (2,3) (23,12) (20,0) (13,4) (24,27) (26,8) (19,10) (1,20) (2,0) (1,19) (11,10) (21,25) (19,23) (24,15) (11,2) (5,18) (9,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph231",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,5) (25,17) (1,3) (14,26) (15,27) (22,26) (27,9) (26,17) (16,10) (13,23) (4,1) (27,25) (21,0) (25,3) (21,14) (25,12) (7,11) (11,25) (10,17) (13,20) (19,17) (14,18) (19,2) (24,16) (6,5) (18,13) (10,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1259",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (25,8) (4,0) (12,27) (0,2) (24,11) (5,21) (7,8) (16,20) (13,18) (10,3) (17,8) (5,0) (19,0) (14,9) (17,2) (25,10) (2,18) (0,1) (5,7) (6,25) (0,16) (23,20) (13,20) (12,15) (15,26) (2,9) (4,1) (11,17) (0,3) (13,26) (23,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph764",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,19) (16,32) (9,30) (19,21) (6,16) (10,2) (13,23) (23,4) (29,27) (14,25) (15,0) (20,17) (12,29) (11,4) (27,15) (7,27) (22,10) (17,21) (24,23) (26,3) (9,28) (18,2) (23,32) (6,30) (22,20) (9,1) (5,14) (0,24) (6,8) (31,1) (5,31) (26,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1612",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (20,29) (22,1) (2,10) (18,1) (15,1) (28,6) (20,4) (3,17) (1,6) (12,3) (7,0) (9,30) (16,14) (25,10) (19,23) (23,8) (16,0) (8,22) (2,22) (27,28) (5,16) (13,12) (9,31) (9,15) (12,5) (24,26) (9,11) (0,2) (0,1) (27,20) (12,9) (24,12) (29,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph54",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,25) (21,17) (16,8) (3,22) (5,24) (21,8) (0,3) (18,22) (2,13) (24,10) (23,13) (14,11) (12,7) (1,16) (4,25) (20,10) (19,17) (13,8) (5,9) (7,0) (15,22) (11,9) (20,25) (12,23) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1943",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,16) (22,20) (11,22) (14,18) (13,33) (2,0) (9,16) (25,10) (26,33) (4,6) (23,17) (16,21) (4,30) (1,26) (12,31) (12,7) (25,20) (3,7) (19,1) (32,5) (6,17) (19,20) (27,6) (6,18) (28,12) (12,8) (29,24) (29,32) (24,4) (15,9) (34,7) (0,3) (34,27) (4,0) (1,6) (33,2) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1212",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,17) (19,4) (0,1) (11,23) (6,14) (27,15) (8,22) (8,16) (26,23) (16,14) (26,10) (4,17) (0,9) (2,23) (12,21) (1,7) (19,11) (24,25) (13,10) (24,22) (20,15) (18,6) (16,0) (17,24) (9,3) (24,5) (15,1) (27,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1853",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,30) (0,2) (11,9) (3,13) (19,30) (21,25) (0,1) (13,28) (32,4) (1,31) (24,0) (27,33) (28,9) (33,7) (21,30) (12,4) (26,23) (5,27) (22,14) (17,29) (15,24) (5,25) (14,32) (1,3) (12,29) (3,32) (21,10) (10,23) (5,14) (20,17) (23,18) (17,6) (9,0) (16,0) (22,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph857",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (30,22) (17,19) (6,31) (17,4) (3,13) (6,26) (5,16) (16,20) (18,1) (18,4) (4,29) (0,23) (32,19) (22,15) (11,21) (2,0) (25,6) (10,14) (2,33) (27,28) (22,27) (24,7) (1,8) (29,27) (13,0) (25,32) (24,23) (9,12) (16,27) (12,25) (1,11) (14,16) (0,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph978",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,14) (11,33) (29,1) (20,7) (27,34) (7,34) (17,24) (3,13) (10,24) (9,12) (30,5) (26,23) (29,17) (22,8) (32,18) (13,26) (9,0) (12,22) (25,6) (13,25) (4,11) (3,16) (29,25) (9,11) (19,13) (31,16) (23,22) (19,14) (7,28) (5,29) (10,7) (15,27) (32,21) (2,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph975",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (19,20) (21,16) (1,19) (3,7) (0,2) (16,26) (30,4) (1,6) (29,24) (11,22) (23,17) (12,31) (2,33) (25,20) (12,7) (15,9) (12,8) (4,24) (16,9) (1,26) (32,5) (33,13) (18,14) (12,28) (7,34) (18,6) (6,27) (10,25) (6,17) (20,22) (29,32) (4,6) (26,33) (27,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1070",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,18) (11,25) (25,12) (1,0) (5,7) (17,25) (0,21) (17,10) (14,20) (6,1) (25,4) (9,10) (2,5) (18,14) (14,24) (25,3) (2,19) (13,19) (3,1) (23,17) (10,16) (8,11) (22,16) (17,15) (13,21) (4,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph882",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (9,6) (1,17) (21,10) (28,13) (14,20) (16,11) (21,0) (17,26) (23,7) (4,12) (27,26) (7,15) (9,3) (20,27) (5,19) (16,32) (0,17) (18,2) (24,23) (22,12) (11,5) (1,19) (28,20) (2,33) (4,31) (18,30) (31,25) (6,17) (32,29) (24,5) (12,8) (12,30) (22,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph0",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,0) (10,13) (4,23) (3,22) (18,21) (0,10) (6,2) (24,15) (20,9) (0,17) (14,13) (1,12) (8,5) (16,22) (20,14) (19,5) (4,19) (25,21) (24,7) (22,4) (21,10) (12,16) (5,14) (6,10) (3,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph700",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,23) (6,12) (19,12) (20,27) (31,29) (7,30) (31,4) (18,16) (31,11) (30,21) (2,10) (11,0) (15,0) (9,32) (14,11) (9,3) (1,23) (5,30) (8,25) (22,19) (8,7) (6,24) (1,19) (28,32) (2,27) (10,16) (15,22) (22,20) (5,26) (5,31) (18,13) (17,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph452",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,2) (6,25) (12,29) (5,24) (13,20) (25,14) (18,2) (19,9) (20,16) (0,22) (7,8) (13,18) (4,1) (9,28) (23,20) (10,3) (17,11) (7,5) (15,29) (27,11) (26,15) (25,23) (29,10) (8,17) (1,0) (8,28) (21,2) (13,26) (0,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1504",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,6) (29,28) (13,14) (0,1) (23,21) (2,0) (2,17) (25,1) (2,22) (26,7) (24,4) (30,18) (5,0) (10,8) (16,27) (26,13) (23,10) (3,26) (9,20) (20,22) (26,9) (18,0) (23,24) (27,28) (3,16) (16,19) (24,15) (23,26) (0,11) (25,12) (3,12) (0,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1804",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,29) (15,7) (9,22) (21,10) (5,11) (26,21) (0,3) (30,5) (4,0) (6,12) (1,0) (25,4) (4,21) (14,0) (24,12) (30,8) (9,18) (4,5) (28,33) (2,17) (15,14) (20,13) (22,20) (0,32) (16,5) (21,14) (1,31) (3,23) (28,12) (2,0) (23,22) (17,27) (6,27) (20,14) (17,21) (31,27) (19,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1747",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,9) (31,29) (25,1) (24,19) (0,17) (1,29) (9,30) (1,9) (5,18) (2,0) (26,6) (3,30) (21,22) (23,16) (23,2) (14,18) (4,30) (8,28) (12,16) (20,19) (16,27) (26,11) (14,7) (14,15) (0,18) (19,14) (1,0) (0,10) (32,16) (23,19) (26,14) (28,1) (13,15) (18,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1803",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,16) (11,24) (0,3) (6,1) (25,0) (18,26) (16,9) (23,22) (0,20) (32,10) (29,7) (30,22) (0,2) (2,32) (14,15) (27,33) (0,6) (27,20) (26,14) (30,16) (22,3) (13,25) (21,12) (1,0) (23,2) (1,19) (4,27) (4,5) (15,12) (31,28) (33,15) (21,8) (22,21) (28,15) (32,29) (17,2) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph363",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,12) (12,1) (19,16) (12,22) (28,16) (5,26) (7,25) (15,19) (14,0) (6,8) (2,5) (26,18) (19,9) (8,1) (13,0) (10,25) (4,20) (6,21) (2,0) (24,16) (19,26) (0,7) (17,3) (20,17) (23,14) (4,2) (11,9) (27,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1870",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (17,1) (8,21) (15,17) (10,29) (15,28) (2,1) (3,14) (19,3) (27,30) (32,2) (20,5) (13,31) (5,4) (27,23) (6,2) (4,18) (13,6) (16,11) (27,14) (16,30) (0,28) (31,23) (18,9) (2,21) (12,25) (26,8) (28,7) (4,19) (0,2) (14,10) (1,0) (12,18) (21,33) (24,5) (22,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1898",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,23) (23,4) (20,10) (20,3) (30,5) (0,1) (21,4) (18,16) (20,17) (3,31) (17,27) (0,10) (32,18) (19,25) (14,1) (13,18) (24,26) (31,26) (32,9) (11,33) (15,30) (13,4) (15,7) (7,20) (19,33) (14,28) (8,11) (3,28) (19,22) (2,17) (6,33) (27,29) (30,12) (33,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph120",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,25) (13,23) (23,1) (24,4) (21,19) (19,16) (24,21) (13,20) (14,4) (21,3) (18,15) (6,26) (1,15) (5,20) (5,16) (17,11) (0,23) (8,6) (7,23) (9,13) (12,1) (13,22) (19,10) (6,2) (24,17) (22,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph762",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (15,26) (28,11) (27,20) (31,2) (18,3) (8,18) (24,23) (6,29) (5,2) (21,9) (17,20) (4,25) (7,31) (18,22) (32,31) (28,7) (28,24) (28,16) (14,20) (10,29) (9,13) (13,26) (16,1) (30,22) (5,6) (15,25) (1,8) (12,8) (7,0) (19,6) (24,17) (32,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1872",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,6) (18,22) (29,18) (0,21) (17,30) (15,12) (12,31) (11,15) (23,30) (12,32) (11,14) (33,20) (16,26) (23,32) (28,3) (9,31) (31,13) (21,4) (24,16) (2,7) (20,7) (15,5) (19,16) (16,0) (28,11) (12,25) (33,21) (1,0) (27,7) (19,13) (8,31) (29,10) (11,1) (10,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph680",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,16) (2,28) (22,19) (21,11) (8,14) (5,27) (12,2) (10,21) (1,0) (5,12) (10,24) (1,15) (6,7) (16,19) (1,13) (20,19) (31,6) (18,31) (4,5) (3,14) (5,19) (5,6) (20,26) (23,2) (29,9) (29,5) (11,7) (19,8) (23,25) (24,17) (31,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1659",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (5,12) (5,0) (0,1) (3,30) (7,10) (8,31) (17,12) (2,16) (13,18) (15,1) (25,28) (1,26) (24,12) (1,5) (6,2) (21,9) (25,7) (18,8) (4,11) (0,30) (4,0) (5,27) (3,0) (0,2) (22,26) (19,13) (12,14) (25,13) (20,17) (23,28) (29,1) (29,25) (16,14) (11,6) (5,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph457",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,27) (16,21) (14,15) (6,18) (2,10) (13,22) (0,24) (0,12) (28,29) (18,24) (2,19) (0,27) (20,15) (25,13) (3,7) (6,26) (23,17) (1,29) (8,20) (22,7) (19,11) (8,18) (10,20) (5,17) (6,1) (3,11) (9,16) (9,24) (29,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1769",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (3,32) (15,0) (11,24) (9,8) (27,32) (23,10) (0,22) (32,4) (13,3) (23,16) (1,3) (24,23) (6,17) (27,5) (30,2) (20,14) (9,28) (30,1) (7,22) (29,21) (0,9) (30,18) (31,14) (25,21) (13,26) (28,12) (1,0) (10,21) (12,4) (25,5) (17,19) (29,17) (14,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1540",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,17) (9,18) (17,23) (30,22) (19,12) (5,2) (1,19) (17,0) (12,18) (21,13) (8,10) (11,10) (13,20) (14,7) (15,23) (0,3) (0,21) (25,28) (13,2) (11,4) (1,0) (24,3) (30,8) (16,14) (29,30) (26,8) (15,25) (16,12) (0,29) (1,25) (27,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1359",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,4) (17,27) (10,6) (23,12) (20,6) (25,3) (3,2) (23,2) (1,0) (12,22) (16,25) (21,1) (21,20) (3,17) (13,16) (24,11) (9,26) (7,10) (8,1) (11,13) (5,0) (14,8) (14,15) (28,26) (5,22) (24,18) (2,0) (23,14) (0,3) (9,7) (0,4) (5,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph338",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,21) (26,3) (14,21) (16,24) (23,13) (10,23) (4,28) (12,9) (21,0) (26,15) (8,26) (21,3) (4,14) (1,22) (11,20) (20,17) (1,20) (23,12) (9,25) (2,19) (25,16) (14,11) (25,19) (18,16) (2,6) (5,19) (14,13) (19,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph578",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (22,4) (24,25) (13,7) (3,16) (24,20) (24,29) (22,16) (26,19) (13,15) (15,8) (6,23) (27,23) (28,11) (29,12) (17,5) (14,17) (10,21) (30,2) (3,25) (30,3) (18,7) (8,23) (18,19) (23,0) (10,14) (26,9) (5,11) (1,14) (17,20) (21,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1134",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,16) (3,4) (3,0) (21,9) (13,0) (16,6) (22,16) (24,25) (8,23) (18,2) (5,20) (12,16) (3,14) (13,11) (26,17) (1,8) (14,5) (15,2) (11,17) (6,14) (9,18) (18,19) (8,13) (15,10) (15,12) (1,0) (24,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1456",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,10) (26,27) (18,2) (0,1) (19,21) (16,25) (13,8) (18,6) (8,25) (16,4) (18,21) (13,0) (29,1) (15,5) (3,18) (15,16) (17,28) (14,25) (21,20) (2,26) (24,22) (25,23) (20,10) (12,18) (3,24) (28,1) (5,26) (7,17) (9,17) (25,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph629",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,9) (22,21) (31,16) (15,5) (13,27) (8,17) (0,24) (16,20) (19,7) (27,4) (6,17) (8,29) (4,26) (2,11) (19,5) (18,7) (20,11) (0,7) (16,14) (4,1) (23,30) (25,18) (30,13) (9,3) (31,12) (26,9) (4,28) (1,21) (26,10) (2,19) (3,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph630",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (26,0) (21,14) (15,24) (6,9) (27,5) (8,24) (16,15) (19,11) (18,17) (3,12) (15,21) (28,19) (25,9) (4,25) (21,5) (29,1) (14,23) (13,26) (21,29) (31,22) (7,29) (28,20) (31,6) (18,19) (3,0) (3,30) (26,24) (10,12) (4,1) (23,2) (19,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1537",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,0) (20,29) (20,30) (26,2) (29,12) (1,0) (25,8) (6,19) (16,7) (1,28) (13,27) (14,4) (8,27) (0,15) (10,17) (6,20) (25,4) (24,3) (23,18) (23,16) (11,25) (15,21) (5,17) (0,24) (2,0) (22,4) (16,19) (17,30) (6,25) (20,2) (0,3) (9,23) (18,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1933",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,17) (11,31) (7,20) (23,2) (24,8) (27,15) (27,9) (0,3) (14,4) (0,2) (32,33) (10,33) (14,32) (12,30) (22,6) (8,29) (1,10) (16,8) (19,23) (25,34) (18,13) (33,23) (32,30) (25,21) (16,26) (0,5) (18,1) (28,9) (31,6) (0,4) (5,32) (24,9) (24,20) (27,11) (0,1) (34,14) (23,27) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1568",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,30) (16,6) (10,3) (26,15) (26,14) (20,8) (29,28) (8,2) (12,8) (21,16) (22,16) (11,16) (6,18) (13,4) (29,26) (16,5) (0,26) (11,4) (10,0) (17,24) (27,22) (0,1) (1,23) (6,2) (19,7) (6,19) (9,25) (1,19) (0,25) (14,24) (4,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1981",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,11) (32,13) (31,30) (8,5) (14,17) (7,29) (3,6) (34,17) (18,1) (24,22) (26,4) (15,28) (15,25) (26,31) (0,2) (0,32) (20,31) (17,21) (25,22) (13,33) (19,23) (34,10) (27,24) (10,25) (3,1) (23,4) (7,32) (15,12) (18,33) (27,16) (3,0) (0,1) (21,2) (11,31) (9,11) (5,0) (20,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph249",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,12) (20,13) (15,19) (4,11) (22,6) (26,25) (2,19) (15,17) (6,7) (27,20) (22,15) (18,3) (15,11) (1,7) (0,18) (17,5) (8,17) (24,17) (19,10) (14,18) (8,21) (2,16) (4,9) (0,26) (20,12) (17,26) (7,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph633",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,9) (15,11) (31,9) (16,12) (19,5) (6,4) (29,30) (17,30) (26,11) (8,27) (0,20) (15,0) (25,21) (22,24) (12,6) (7,16) (10,2) (1,12) (14,25) (18,9) (23,28) (13,6) (21,26) (11,23) (19,24) (3,13) (22,27) (23,3) (29,18) (27,11) (12,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph660",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,15) (26,16) (24,13) (22,31) (23,31) (4,2) (25,0) (28,0) (20,1) (7,23) (11,3) (22,15) (10,19) (14,12) (9,1) (4,18) (14,21) (18,5) (26,1) (17,16) (20,5) (22,6) (23,14) (22,17) (9,19) (23,28) (21,8) (24,29) (8,11) (27,4) (14,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph649",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,7) (22,8) (12,22) (18,10) (4,23) (19,20) (14,16) (21,20) (5,25) (9,11) (31,25) (2,7) (15,26) (6,4) (19,1) (26,1) (2,0) (29,24) (3,12) (12,7) (16,9) (25,27) (17,6) (17,18) (24,4) (13,6) (16,20) (12,28) (27,6) (30,26) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1391",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,27) (22,5) (19,17) (10,2) (12,27) (0,1) (16,14) (23,14) (6,19) (28,21) (14,3) (23,1) (10,0) (1,26) (9,8) (28,13) (21,15) (23,13) (2,25) (0,18) (12,5) (17,10) (4,5) (20,16) (11,7) (4,8) (19,24) (22,19) (22,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph550",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,28) (1,0) (7,5) (27,23) (20,16) (8,17) (29,14) (13,20) (17,2) (26,15) (12,29) (16,0) (9,21) (13,18) (0,24) (19,25) (8,7) (5,25) (3,10) (25,10) (29,8) (11,17) (13,26) (30,6) (1,4) (28,11) (20,23) (15,30) (22,2) (2,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1510",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (30,13) (11,5) (21,28) (4,26) (24,30) (8,11) (17,7) (13,2) (30,23) (3,10) (12,22) (0,19) (11,12) (2,0) (16,18) (25,30) (3,4) (28,9) (19,11) (29,18) (9,10) (6,18) (8,3) (16,26) (1,0) (14,0) (0,20) (2,27) (1,16) (24,0) (28,7) (26,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1220",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,0) (6,7) (2,16) (9,4) (0,1) (18,14) (19,2) (18,3) (17,26) (17,15) (19,15) (26,0) (26,25) (7,23) (8,17) (15,22) (17,5) (21,8) (13,20) (15,12) (11,4) (20,27) (19,10) (6,22) (17,24) (15,11) (7,1) (20,12) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph163",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,17) (13,5) (14,12) (7,1) (4,24) (12,25) (15,13) (24,2) (9,4) (15,11) (4,16) (18,11) (21,9) (3,24) (19,3) (8,1) (26,17) (20,26) (19,25) (0,12) (9,23) (16,6) (25,8) (6,18) (10,16) (22,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph140",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,20) (2,7) (8,20) (1,4) (25,16) (15,16) (7,23) (13,1) (2,10) (13,26) (6,0) (21,26) (15,10) (18,3) (14,6) (5,24) (14,26) (1,11) (12,15) (19,15) (23,11) (22,8) (18,0) (17,18) (13,9) (1,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1247",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,20) (12,3) (1,0) (6,19) (11,19) (2,1) (9,15) (7,16) (5,16) (23,24) (11,12) (23,20) (21,12) (20,3) (25,5) (0,27) (27,23) (18,26) (0,8) (22,0) (9,13) (15,10) (16,19) (11,1) (12,26) (10,17) (14,7) (18,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1871",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,25) (23,20) (20,13) (28,20) (1,27) (28,21) (25,4) (18,32) (10,26) (11,3) (5,11) (29,0) (31,1) (19,4) (22,29) (31,15) (23,33) (18,12) (20,7) (0,4) (9,8) (5,30) (14,1) (0,32) (10,21) (0,2) (22,16) (27,9) (6,13) (0,1) (2,31) (22,17) (21,11) (24,21) (18,21) (3,0) (18,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1195",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,21) (6,8) (21,25) (0,2) (13,7) (3,5) (20,21) (13,17) (15,19) (16,19) (6,20) (0,1) (12,8) (4,0) (14,10) (3,0) (19,1) (5,14) (18,8) (1,9) (13,15) (1,5) (13,11) (22,5) (0,5) (4,24) (3,2) (24,14) (26,3) (9,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph902",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (15,11) (19,13) (32,12) (1,11) (18,22) (30,10) (12,31) (13,31) (11,29) (33,20) (10,15) (8,31) (7,20) (16,0) (16,24) (30,17) (29,18) (4,21) (16,27) (11,14) (12,6) (34,25) (28,7) (28,3) (7,2) (16,19) (9,31) (25,21) (33,23) (12,26) (5,15) (21,0) (23,32) (15,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1249",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,26) (25,3) (23,21) (18,3) (18,9) (20,12) (15,1) (10,0) (18,22) (27,16) (8,19) (11,9) (26,23) (24,4) (3,13) (3,0) (0,2) (27,26) (2,12) (1,9) (15,14) (0,4) (24,17) (6,0) (24,27) (18,21) (1,8) (1,0) (27,6) (26,5) (20,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph861",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (28,14) (13,32) (13,33) (28,5) (25,10) (7,1) (19,14) (15,13) (16,2) (7,6) (5,7) (8,20) (17,8) (25,21) (23,25) (21,31) (18,7) (12,30) (13,12) (8,3) (26,13) (1,25) (33,24) (29,21) (23,15) (9,22) (0,4) (30,0) (3,2) (14,8) (27,26) (9,2) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1626",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,21) (8,7) (18,6) (0,1) (29,21) (15,1) (31,30) (27,12) (23,19) (3,14) (0,2) (1,23) (16,13) (9,11) (25,23) (21,8) (26,21) (10,4) (5,10) (3,28) (17,16) (10,21) (18,9) (5,20) (17,23) (22,0) (0,6) (4,30) (24,0) (1,3) (20,15) (6,31) (27,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1482",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,8) (1,0) (2,0) (20,1) (5,3) (19,8) (13,7) (13,17) (5,1) (20,6) (4,24) (2,3) (21,3) (28,22) (9,1) (5,25) (10,14) (9,26) (15,3) (15,29) (18,19) (6,23) (11,13) (3,0) (5,14) (0,4) (8,12) (24,21) (15,13) (27,14) (16,19) (28,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph875",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,10) (23,32) (10,16) (12,10) (28,27) (16,5) (12,14) (33,4) (25,10) (21,20) (4,19) (1,7) (29,22) (13,2) (13,8) (20,10) (9,17) (31,29) (0,18) (3,24) (20,13) (5,15) (11,6) (2,23) (28,0) (31,19) (33,1) (31,26) (4,21) (5,30) (7,24) (18,9) (19,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph955",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,10) (28,21) (21,20) (20,8) (16,4) (27,5) (2,12) (7,6) (6,4) (19,28) (20,26) (25,31) (30,18) (12,24) (13,15) (17,8) (6,5) (14,26) (11,10) (22,26) (0,9) (5,25) (32,13) (21,27) (12,34) (12,5) (9,20) (29,33) (30,31) (33,6) (1,26) (16,3) (15,2) (23,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1130",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,8) (4,21) (11,22) (3,25) (0,5) (8,0) (2,15) (12,24) (23,21) (17,4) (1,16) (25,6) (3,0) (26,7) (4,0) (8,15) (18,5) (23,13) (9,2) (11,10) (6,23) (0,2) (19,18) (0,1) (15,18) (24,20) (26,13) (25,15) (0,24) (10,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph273",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,6) (24,20) (13,7) (15,8) (12,3) (4,23) (13,15) (27,19) (2,22) (7,18) (5,11) (25,24) (23,8) (21,22) (17,5) (17,20) (17,14) (3,19) (14,1) (21,10) (9,16) (23,11) (25,27) (24,26) (0,23) (14,10) (18,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1231",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,16) (26,19) (26,7) (11,20) (2,5) (26,10) (9,12) (8,23) (14,27) (1,0) (9,25) (21,14) (12,23) (18,1) (2,19) (3,24) (3,21) (16,22) (25,16) (20,15) (21,0) (13,23) (1,20) (14,11) (19,25) (13,14) (19,4) (21,6) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1835",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,1) (6,27) (17,23) (1,26) (22,11) (10,25) (15,9) (17,6) (21,16) (5,0) (3,0) (14,18) (13,33) (4,30) (19,1) (26,32) (19,20) (26,16) (2,0) (22,20) (4,24) (7,12) (16,9) (31,12) (4,0) (1,0) (18,6) (7,3) (24,29) (12,28) (4,6) (8,12) (33,27) (25,20) (33,2) (29,7) (32,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph135",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,11) (13,23) (8,11) (3,23) (21,18) (7,21) (25,1) (22,11) (22,4) (3,10) (9,16) (16,5) (20,11) (8,24) (5,7) (14,22) (25,12) (19,4) (0,6) (1,15) (26,7) (0,17) (2,6) (12,8) (0,1) (14,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph170",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,23) (20,17) (11,10) (8,2) (5,15) (6,10) (20,21) (0,8) (5,25) (19,7) (17,4) (13,6) (4,7) (24,15) (16,21) (26,6) (3,9) (7,12) (0,26) (18,17) (0,16) (25,1) (26,25) (22,19) (3,14) (15,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1805",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,12) (29,8) (0,26) (2,0) (25,14) (13,33) (9,28) (14,23) (10,33) (20,4) (29,11) (6,14) (14,19) (0,3) (2,16) (12,30) (21,17) (21,16) (15,28) (31,23) (8,22) (2,26) (22,23) (1,18) (28,33) (18,27) (5,32) (14,32) (27,10) (28,25) (0,1) (8,7) (3,18) (7,30) (4,29) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph719",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,19) (1,4) (23,27) (14,17) (27,1) (13,22) (11,16) (19,28) (12,11) (21,16) (16,1) (7,30) (10,7) (24,3) (26,29) (18,20) (21,20) (17,3) (25,19) (0,8) (20,3) (25,11) (7,3) (9,32) (22,11) (31,9) (26,12) (6,28) (11,8) (2,15) (15,5) (14,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph622",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,24) (0,20) (14,16) (12,22) (8,26) (20,3) (5,12) (30,8) (12,1) (9,14) (24,9) (6,2) (24,0) (29,14) (7,26) (10,0) (7,19) (14,6) (28,25) (14,13) (22,10) (18,27) (4,27) (31,14) (21,4) (30,23) (11,29) (22,7) (29,17) (30,27) (28,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1507",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (14,9) (8,11) (5,7) (21,26) (12,5) (12,25) (4,8) (15,1) (23,29) (0,20) (2,26) (19,8) (2,6) (29,27) (15,7) (17,22) (23,2) (20,29) (26,15) (13,30) (30,18) (7,28) (26,24) (10,17) (11,26) (10,8) (18,20) (22,3) (9,6) (16,2) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1969",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,30) (21,9) (20,14) (28,11) (16,28) (33,1) (10,29) (4,25) (15,26) (13,26) (32,27) (31,4) (8,12) (2,0) (7,0) (7,31) (8,4) (20,29) (18,3) (18,8) (6,19) (23,24) (9,13) (31,2) (7,28) (17,20) (2,5) (28,24) (8,34) (18,22) (32,22) (1,0) (5,6) (1,16) (17,24) (3,0) (25,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph255",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,15) (18,19) (21,9) (25,24) (16,12) (2,15) (5,14) (2,18) (17,27) (15,10) (6,16) (13,0) (13,11) (8,1) (16,22) (27,24) (4,3) (8,13) (23,8) (18,9) (14,6) (20,5) (0,3) (7,16) (14,3) (0,26) (11,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1802",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (17,9) (21,1) (9,26) (15,5) (20,33) (4,29) (11,2) (2,0) (20,11) (17,8) (27,13) (4,26) (31,13) (5,19) (9,3) (32,16) (4,27) (31,12) (0,25) (4,1) (0,3) (24,30) (0,1) (30,8) (7,19) (17,6) (23,21) (18,28) (19,2) (16,14) (22,16) (0,7) (3,2) (7,18) (20,22) (10,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph624",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,20) (28,9) (1,3) (2,23) (29,8) (9,27) (27,23) (31,6) (13,27) (6,22) (10,1) (30,7) (31,25) (12,18) (24,9) (18,24) (25,21) (16,8) (30,11) (11,27) (14,23) (19,1) (14,4) (5,20) (15,14) (24,8) (10,23) (2,0) (15,17) (16,26) (25,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1966",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,33) (27,23) (21,10) (10,11) (26,23) (10,15) (1,20) (19,3) (34,9) (31,29) (9,14) (10,28) (30,7) (33,5) (29,4) (10,17) (4,27) (22,10) (11,33) (14,32) (3,2) (9,7) (0,26) (6,12) (1,0) (2,17) (1,10) (26,2) (4,16) (21,18) (25,30) (8,17) (11,14) (30,13) (26,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph427",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,16) (19,1) (14,3) (29,5) (27,29) (9,6) (25,20) (9,20) (6,22) (11,8) (28,27) (21,18) (14,2) (9,26) (29,10) (26,23) (23,19) (27,21) (4,9) (14,0) (15,8) (24,2) (21,7) (12,15) (2,26) (7,1) (2,17) (21,13) (23,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph125",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,4) (23,11) (2,7) (2,10) (16,25) (25,20) (15,19) (6,14) (6,0) (26,14) (21,26) (12,15) (1,11) (1,13) (3,18) (5,1) (8,22) (0,18) (26,13) (8,20) (7,23) (13,9) (5,24) (15,16) (10,15) (17,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1050",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,20) (18,0) (11,9) (10,3) (25,12) (5,0) (18,16) (23,24) (4,0) (8,11) (11,0) (3,0) (24,17) (7,10) (23,8) (6,4) (15,14) (2,0) (22,1) (6,25) (3,21) (7,25) (15,21) (19,17) (20,2) (1,13) (0,1) (5,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1577",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,7) (13,30) (19,2) (24,30) (23,16) (4,8) (12,17) (3,11) (5,3) (26,0) (30,17) (18,26) (15,27) (20,29) (14,24) (23,19) (6,23) (11,15) (8,11) (25,14) (3,0) (0,1) (20,1) (5,28) (10,22) (9,25) (0,2) (21,20) (1,28) (12,7) (22,29) (7,27) (16,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph130",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,9) (23,25) (11,16) (17,21) (24,6) (11,26) (18,1) (8,19) (11,2) (13,20) (14,23) (5,13) (18,21) (26,7) (19,6) (20,12) (4,2) (23,16) (21,5) (5,10) (15,25) (12,25) (3,2) (0,1) (22,9) (1,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph185",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,15) (23,0) (26,25) (26,6) (24,25) (24,23) (5,11) (24,20) (7,18) (1,14) (10,21) (15,13) (11,22) (17,14) (23,4) (9,16) (10,14) (22,2) (12,3) (20,17) (5,17) (3,19) (8,23) (13,7) (18,16) (21,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph903",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,24) (21,5) (30,20) (32,33) (14,7) (31,23) (12,4) (12,26) (26,13) (25,2) (8,5) (0,17) (5,30) (20,25) (13,24) (12,28) (11,21) (10,15) (3,24) (34,0) (14,8) (11,6) (9,13) (29,11) (15,16) (18,33) (27,31) (29,9) (5,22) (5,33) (2,17) (34,19) (1,25) (23,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph580",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,24) (18,17) (11,21) (29,16) (13,11) (22,8) (14,13) (30,5) (25,29) (20,12) (7,26) (19,1) (16,30) (27,9) (4,17) (11,15) (17,24) (0,17) (22,26) (0,11) (28,6) (1,12) (27,30) (23,30) (5,7) (30,10) (12,3) (19,28) (12,7) (2,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph475",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (19,18) (18,11) (25,12) (27,15) (7,6) (28,27) (0,6) (21,23) (29,16) (10,3) (17,27) (26,4) (22,7) (24,14) (24,13) (17,7) (12,17) (28,8) (11,20) (21,18) (5,3) (9,6) (22,1) (7,24) (27,26) (21,24) (29,19) (2,19) (14,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph910",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,0) (31,22) (1,18) (24,7) (6,28) (18,4) (1,8) (15,16) (25,13) (16,20) (14,10) (29,4) (11,24) (17,4) (29,27) (0,23) (11,1) (21,22) (0,20) (2,12) (9,12) (3,13) (0,2) (26,23) (19,32) (32,25) (22,27) (25,6) (19,17) (6,33) (27,16) (5,16) (30,27) (12,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph79",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,20) (13,8) (17,9) (20,10) (3,23) (25,1) (15,16) (16,4) (3,18) (5,15) (6,18) (2,18) (22,25) (0,13) (24,16) (25,14) (21,17) (19,24) (10,1) (7,17) (11,25) (2,5) (25,8) (18,21) (18,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph368",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,24) (28,3) (12,7) (5,3) (10,22) (19,20) (14,24) (26,13) (15,27) (14,22) (18,23) (25,5) (9,25) (17,3) (26,11) (19,2) (16,21) (11,8) (1,28) (17,12) (27,7) (11,15) (23,6) (0,16) (8,4) (20,1) (26,0) (23,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph354",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,7) (1,20) (16,0) (18,3) (15,20) (19,4) (14,26) (9,21) (6,18) (21,24) (11,22) (23,4) (7,9) (6,20) (17,21) (4,1) (5,28) (28,8) (25,14) (1,12) (28,6) (16,28) (2,14) (16,10) (26,0) (8,11) (27,23) (23,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph197",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (12,17) (23,5) (2,7) (3,8) (1,6) (4,5) (14,12) (13,22) (26,2) (15,10) (26,13) (16,9) (18,1) (13,16) (25,21) (19,4) (0,14) (1,17) (11,14) (24,20) (25,1) (0,20) (23,8) (15,11) (7,0) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph675",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,11) (24,6) (16,13) (14,9) (7,1) (4,17) (10,25) (27,26) (25,19) (11,15) (22,28) (20,0) (8,12) (5,24) (13,2) (29,27) (22,14) (6,25) (12,0) (0,31) (16,3) (23,21) (6,30) (0,23) (1,18) (16,20) (16,27) (29,4) (4,18) (27,22) (19,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1010",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,13) (25,9) (7,21) (0,1) (25,6) (13,23) (15,10) (10,4) (15,18) (20,10) (3,0) (2,24) (20,17) (18,21) (1,23) (14,18) (14,13) (6,13) (4,3) (16,8) (2,3) (24,11) (21,8) (2,0) (5,22) (4,12) (19,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph398",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,11) (18,25) (8,11) (23,11) (26,8) (28,7) (21,22) (27,12) (21,19) (2,6) (7,5) (1,28) (7,24) (0,17) (13,23) (3,25) (5,16) (0,6) (4,27) (3,10) (8,12) (20,4) (9,16) (10,14) (15,1) (22,14) (1,0) (22,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1316",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,4) (8,4) (16,7) (13,21) (22,11) (19,6) (0,1) (4,19) (17,4) (7,13) (22,6) (4,24) (17,9) (12,5) (6,27) (3,1) (7,2) (18,20) (5,15) (6,0) (23,3) (2,0) (13,0) (28,2) (25,12) (14,24) (26,5) (19,10) (0,4) (14,20) (0,3) (6,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1095",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (0,1) (0,4) (5,16) (8,2) (12,7) (11,10) (24,17) (11,20) (7,5) (12,3) (18,16) (11,0) (13,11) (19,24) (25,4) (15,12) (17,6) (23,7) (17,21) (8,22) (18,0) (1,19) (13,9) (12,1) (12,22) (17,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1383",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,9) (13,12) (17,25) (1,17) (10,25) (9,6) (9,27) (3,0) (21,0) (24,2) (15,7) (20,24) (8,6) (2,10) (7,9) (11,3) (21,28) (15,14) (2,0) (18,9) (4,14) (12,5) (16,7) (27,26) (7,10) (1,11) (0,1) (13,26) (26,22) (4,0) (14,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph420",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,25) (21,10) (24,7) (12,13) (1,2) (18,11) (27,17) (11,19) (6,22) (28,24) (22,3) (18,26) (29,5) (15,23) (9,11) (16,0) (20,22) (3,14) (9,1) (4,14) (17,28) (8,4) (16,13) (5,12) (27,19) (0,25) (19,14) (13,24) (19,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1113",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,3) (24,20) (26,6) (0,1) (21,6) (4,2) (11,21) (13,14) (17,10) (2,0) (8,22) (20,17) (22,23) (19,7) (24,19) (12,9) (2,13) (1,15) (25,24) (20,4) (6,0) (25,18) (20,3) (6,14) (26,22) (12,0) (8,15) (25,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1629",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,3) (4,19) (25,4) (25,8) (20,28) (0,2) (9,27) (1,14) (13,20) (11,21) (20,7) (9,8) (1,29) (22,29) (21,18) (15,31) (18,12) (18,25) (11,5) (2,31) (17,22) (0,4) (0,1) (24,10) (5,0) (31,20) (27,1) (28,21) (0,26) (21,23) (13,6) (16,22) (10,21) (30,18) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1251",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,6) (0,11) (22,23) (5,22) (21,27) (18,25) (0,4) (25,9) (20,11) (17,20) (19,8) (0,16) (2,0) (1,6) (23,12) (24,0) (0,5) (21,8) (7,12) (1,0) (21,9) (2,11) (3,0) (26,5) (12,10) (2,26) (3,27) (0,13) (14,6) (15,18) (8,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1799",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (24,17) (5,24) (4,13) (10,20) (9,28) (18,27) (15,0) (1,15) (9,26) (3,7) (16,3) (6,7) (23,4) (17,22) (28,25) (20,29) (21,18) (1,8) (10,16) (7,1) (2,31) (24,19) (10,14) (23,30) (0,1) (9,32) (6,9) (8,30) (12,14) (21,11) (13,18) (27,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1067",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,19) (20,14) (22,16) (8,5) (3,7) (11,0) (10,0) (22,3) (7,24) (12,1) (6,2) (21,10) (4,22) (20,9) (4,23) (10,13) (0,2) (18,21) (1,0) (17,0) (0,3) (12,16) (24,15) (14,5) (13,14) (10,6) (19,5) (21,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1595",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,28) (15,3) (9,27) (15,13) (20,6) (2,0) (8,12) (24,4) (11,13) (5,14) (17,19) (13,7) (21,29) (9,1) (30,15) (6,24) (26,5) (0,4) (21,25) (21,3) (29,8) (14,10) (18,13) (3,0) (22,19) (14,28) (5,1) (1,20) (5,3) (2,3) (8,19) (0,1) (30,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph136",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (21,0) (7,11) (14,19) (6,5) (10,17) (2,5) (10,16) (17,24) (3,25) (9,25) (17,25) (14,26) (11,25) (22,26) (4,1) (18,14) (13,15) (2,19) (20,26) (12,17) (25,14) (3,1) (10,8) (21,13) (18,13) (23,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph691",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,6) (6,31) (2,4) (1,0) (27,7) (24,7) (8,18) (0,13) (8,23) (4,23) (8,24) (29,28) (12,28) (19,30) (27,5) (17,11) (3,19) (1,23) (29,13) (29,25) (30,20) (16,15) (19,31) (18,14) (29,11) (9,15) (10,26) (20,13) (22,10) (4,21) (26,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph836",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,5) (0,31) (21,13) (11,25) (25,13) (6,10) (7,24) (4,30) (28,18) (4,3) (2,7) (14,26) (8,7) (21,18) (11,9) (12,5) (5,33) (25,23) (18,29) (2,20) (32,5) (30,14) (4,31) (10,19) (10,27) (10,3) (9,16) (22,1) (4,7) (22,23) (30,13) (15,22) (7,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1746",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (31,30) (11,22) (0,15) (4,15) (2,24) (2,22) (0,21) (26,7) (28,20) (30,10) (18,26) (0,27) (10,28) (6,30) (11,19) (12,26) (2,13) (1,0) (2,7) (24,23) (26,31) (17,14) (28,25) (32,3) (8,16) (32,24) (5,3) (14,29) (9,23) (8,10) (4,10) (31,17) (1,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1691",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (7,28) (19,21) (22,3) (23,4) (20,7) (1,14) (11,6) (13,4) (17,25) (7,23) (0,10) (30,18) (27,15) (16,26) (4,12) (5,30) (31,17) (0,1) (18,11) (19,31) (28,10) (3,0) (18,13) (26,20) (2,0) (19,14) (27,24) (3,20) (17,2) (9,30) (17,15) (29,3) (20,8) (15,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph566",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (30,28) (1,19) (7,1) (14,2) (21,13) (8,11) (15,12) (21,27) (20,9) (27,30) (12,23) (29,27) (9,26) (26,23) (14,3) (6,9) (10,29) (6,22) (19,23) (21,18) (0,14) (16,2) (9,4) (2,17) (8,15) (29,5) (7,21) (26,2) (2,24) (25,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1967",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,16) (13,30) (4,32) (3,10) (31,0) (5,33) (18,28) (2,7) (13,25) (27,10) (13,21) (7,17) (21,31) (30,14) (2,0) (26,14) (1,22) (4,7) (11,9) (2,20) (19,10) (22,23) (7,24) (23,25) (18,5) (7,8) (5,12) (10,6) (4,3) (18,29) (18,34) (0,1) (3,0) (11,25) (6,5) (15,22) (4,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph326",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,23) (11,7) (27,12) (28,7) (15,1) (11,23) (21,22) (5,16) (8,26) (17,0) (4,20) (9,16) (2,6) (25,18) (10,3) (11,8) (11,22) (7,5) (27,4) (24,7) (14,22) (3,25) (10,14) (21,19) (0,6) (1,0) (28,1) (12,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph385",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,3) (11,17) (0,16) (15,16) (26,2) (15,27) (28,7) (7,10) (24,0) (13,9) (3,0) (6,2) (18,16) (1,18) (5,20) (24,28) (5,11) (15,26) (19,5) (5,21) (8,23) (22,0) (28,9) (27,5) (21,14) (8,20) (12,14) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph834",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,32) (10,25) (14,3) (21,13) (7,29) (5,27) (20,0) (8,18) (26,18) (17,3) (24,26) (25,3) (7,9) (2,13) (6,16) (4,28) (25,32) (3,27) (4,15) (19,7) (23,6) (2,8) (33,19) (3,11) (30,14) (2,14) (5,22) (23,27) (26,9) (12,4) (3,31) (9,1) (15,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1294",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,21) (0,2) (19,25) (4,15) (9,17) (17,18) (0,4) (1,6) (14,16) (13,7) (8,18) (17,4) (0,22) (23,2) (27,12) (0,26) (26,20) (20,7) (11,18) (16,18) (24,10) (3,2) (25,2) (0,1) (26,1) (25,1) (5,12) (10,20) (27,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1387",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,28) (0,3) (7,12) (1,26) (0,2) (0,1) (1,18) (16,21) (11,19) (20,3) (25,28) (17,24) (16,22) (2,5) (22,8) (23,10) (9,4) (3,10) (4,6) (27,15) (25,24) (22,28) (1,16) (17,0) (14,23) (0,19) (2,6) (15,11) (0,13) (15,7) (26,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1101",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,15) (5,21) (23,1) (25,17) (6,15) (6,24) (20,25) (6,18) (11,9) (0,1) (2,22) (2,7) (3,14) (12,10) (20,16) (26,20) (26,2) (1,12) (4,11) (13,4) (5,9) (4,8) (14,1) (0,15) (19,6) (1,13) (9,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1244",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (6,1) (4,3) (26,16) (21,15) (9,6) (27,19) (24,27) (17,15) (12,10) (16,12) (11,2) (23,13) (2,8) (9,2) (4,23) (12,22) (5,9) (23,14) (23,10) (11,23) (17,24) (21,20) (12,25) (1,0) (0,3) (17,13) (18,5) (7,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1656",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,2) (23,5) (1,0) (26,3) (3,16) (24,11) (10,28) (31,0) (22,9) (25,9) (29,22) (10,2) (24,8) (5,6) (31,20) (11,20) (13,12) (30,1) (12,30) (4,29) (17,13) (21,19) (1,29) (2,1) (24,22) (12,19) (3,5) (11,18) (27,14) (7,8) (28,14) (19,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph254",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,5) (9,2) (21,20) (25,16) (27,13) (19,16) (15,8) (20,5) (1,5) (4,7) (21,26) (18,17) (14,9) (10,21) (12,20) (23,19) (15,16) (7,26) (11,8) (6,26) (14,15) (2,20) (0,18) (24,10) (20,3) (17,16) (13,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph424",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,27) (0,21) (10,16) (0,27) (5,26) (13,15) (28,23) (1,23) (5,11) (18,16) (28,8) (22,12) (11,23) (14,23) (4,8) (7,28) (1,29) (27,3) (6,14) (14,20) (6,9) (17,22) (29,22) (19,2) (11,16) (25,29) (23,19) (1,24) (15,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1278",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (9,8) (1,4) (21,18) (11,2) (16,25) (1,19) (17,21) (14,5) (20,13) (25,12) (15,23) (18,1) (20,12) (23,27) (6,26) (2,7) (0,3) (13,5) (25,23) (0,27) (0,2) (3,27) (0,1) (22,27) (5,21) (6,19) (26,11) (0,4) (2,10) (19,8) (24,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph702",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,20) (20,27) (8,6) (14,7) (25,32) (18,32) (24,21) (6,17) (9,21) (22,12) (13,28) (4,29) (17,26) (1,19) (16,11) (31,24) (2,9) (5,23) (4,12) (17,0) (12,30) (22,13) (15,0) (5,19) (7,23) (3,12) (5,11) (31,16) (20,10) (26,27) (1,17) (30,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph8",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,21) (16,14) (20,14) (23,5) (8,9) (23,11) (5,15) (12,14) (10,7) (19,15) (7,25) (0,2) (8,25) (5,25) (17,18) (9,1) (16,4) (22,2) (24,2) (22,11) (13,9) (25,4) (3,17) (6,13) (3,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph106",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (21,15) (6,19) (21,24) (6,20) (14,26) (11,22) (1,10) (7,9) (7,12) (14,2) (17,6) (16,0) (1,20) (16,23) (3,18) (26,19) (8,11) (14,24) (21,9) (23,8) (4,1) (13,20) (16,5) (18,4) (0,25) (4,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph808",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,24) (22,21) (17,2) (12,21) (1,6) (33,27) (23,22) (6,0) (7,29) (26,14) (15,14) (18,26) (15,12) (2,32) (29,32) (20,27) (24,16) (30,22) (1,19) (10,32) (3,22) (25,0) (23,2) (21,8) (28,15) (5,4) (28,31) (13,25) (4,27) (9,16) (20,0) (16,30) (33,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1944",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (33,1) (21,4) (3,24) (13,2) (10,25) (13,20) (13,8) (9,18) (6,11) (31,26) (10,20) (28,27) (19,28) (29,22) (18,0) (34,32) (29,31) (5,16) (34,4) (7,24) (2,23) (10,11) (30,5) (19,4) (23,33) (28,0) (31,19) (9,17) (16,10) (12,14) (10,12) (7,1) (5,15) (1,0) (21,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1580",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,15) (10,2) (27,5) (28,7) (5,21) (23,0) (3,27) (15,29) (1,29) (0,16) (14,13) (4,0) (22,5) (9,14) (5,6) (5,20) (11,18) (28,9) (20,8) (1,0) (8,26) (24,30) (0,3) (2,26) (4,18) (16,15) (7,12) (0,24) (21,17) (11,5) (19,16) (30,25) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1104",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,1) (5,17) (2,16) (23,17) (19,2) (12,15) (24,26) (4,11) (0,26) (20,8) (19,15) (14,18) (25,17) (18,3) (19,10) (4,9) (17,15) (21,7) (6,22) (8,17) (7,6) (7,1) (0,18) (11,15) (20,13) (22,15) (26,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1076",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,4) (22,15) (24,21) (7,4) (13,3) (3,5) (0,4) (24,16) (4,19) (0,1) (23,17) (15,0) (18,4) (0,3) (12,8) (7,17) (17,3) (12,4) (4,1) (1,22) (11,1) (23,25) (21,10) (6,24) (0,2) (23,20) (7,14) (1,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1828",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,16) (19,18) (29,10) (10,16) (22,28) (29,31) (23,27) (5,19) (4,17) (17,21) (19,9) (22,32) (1,0) (23,4) (11,27) (5,8) (20,27) (26,29) (12,1) (2,13) (30,17) (27,0) (7,6) (30,19) (26,2) (27,1) (27,33) (1,24) (0,2) (23,15) (13,22) (31,14) (7,17) (3,0) (3,11) (25,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph796",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (17,23) (23,24) (1,7) (15,28) (5,10) (5,30) (32,30) (23,29) (17,21) (9,25) (19,16) (8,28) (26,6) (0,13) (29,1) (22,4) (3,11) (12,19) (18,13) (20,19) (6,7) (32,4) (16,31) (27,4) (13,7) (3,4) (6,27) (24,2) (22,14) (11,8) (18,31) (9,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1317",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (0,2) (4,27) (1,12) (23,4) (10,12) (9,17) (2,10) (22,15) (24,20) (16,9) (12,27) (24,25) (28,23) (18,0) (5,6) (18,11) (12,8) (22,18) (0,26) (4,14) (21,7) (23,19) (21,26) (7,3) (0,1) (5,28) (7,24) (28,13) (8,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1156",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,0) (7,11) (23,13) (7,5) (25,1) (24,8) (22,14) (11,22) (2,0) (21,7) (3,23) (5,16) (12,25) (2,6) (26,7) (3,10) (0,3) (19,4) (0,6) (4,22) (15,1) (1,0) (11,20) (11,8) (12,8) (18,21) (14,10) (9,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph223",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,27) (26,23) (24,17) (21,18) (25,3) (20,13) (1,8) (21,23) (8,19) (13,3) (22,18) (15,1) (3,18) (9,11) (24,27) (10,0) (20,12) (27,16) (18,9) (0,6) (24,4) (5,26) (7,26) (1,9) (6,27) (12,2) (14,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph503",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,18) (4,1) (12,24) (28,10) (0,11) (4,23) (15,26) (14,3) (26,2) (27,22) (12,8) (20,23) (19,24) (11,28) (15,16) (9,26) (22,17) (26,7) (3,28) (29,22) (29,3) (21,10) (2,24) (16,30) (17,13) (20,17) (0,8) (28,6) (6,5) (25,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1893",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (4,13) (6,33) (23,4) (26,24) (4,21) (18,16) (30,5) (15,7) (7,20) (33,19) (10,20) (15,30) (12,30) (8,11) (13,18) (18,32) (14,1) (14,28) (0,10) (9,32) (31,3) (20,3) (33,20) (22,19) (29,27) (0,1) (20,17) (27,17) (3,28) (33,11) (17,2) (31,26) (19,25) (7,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph793",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,27) (20,27) (26,28) (8,29) (20,7) (24,8) (18,3) (16,22) (9,12) (10,14) (16,5) (31,14) (18,13) (30,27) (11,19) (4,21) (32,7) (23,31) (17,0) (8,16) (17,9) (1,18) (4,13) (11,6) (25,0) (8,11) (16,2) (15,14) (27,28) (5,9) (27,1) (14,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph266",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,15) (26,23) (14,20) (14,3) (17,8) (21,14) (0,19) (16,12) (10,9) (19,25) (16,1) (7,11) (7,9) (4,21) (5,18) (10,6) (11,23) (24,26) (9,21) (15,12) (10,0) (17,13) (4,27) (2,26) (24,22) (0,17) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1508",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,1) (14,0) (0,1) (7,4) (12,2) (30,8) (6,16) (11,5) (4,19) (3,7) (25,14) (6,18) (22,12) (28,6) (29,18) (25,7) (12,9) (13,22) (0,2) (26,28) (4,10) (3,0) (6,11) (15,27) (0,20) (15,2) (23,20) (12,14) (15,30) (16,21) (1,17) (12,26) (15,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph895",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,4) (17,21) (33,28) (16,5) (31,1) (10,21) (27,31) (8,30) (20,13) (6,19) (24,12) (21,4) (7,15) (15,14) (0,32) (26,21) (14,0) (27,17) (14,20) (2,17) (9,18) (20,22) (9,22) (29,27) (22,23) (27,6) (12,28) (5,11) (30,5) (6,12) (14,21) (4,5) (3,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1084",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,3) (2,18) (1,10) (18,6) (16,4) (25,14) (19,24) (13,0) (17,21) (2,5) (11,25) (21,20) (18,21) (16,15) (22,25) (13,8) (9,17) (16,24) (0,1) (25,1) (25,8) (23,3) (20,10) (17,7) (15,5) (12,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1655",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,0) (12,27) (30,31) (21,26) (9,25) (15,14) (14,17) (12,29) (5,7) (21,20) (14,10) (26,28) (26,11) (23,28) (27,19) (12,22) (4,18) (5,31) (19,17) (2,6) (2,1) (16,22) (18,5) (3,0) (3,22) (14,26) (26,30) (10,24) (27,25) (0,1) (13,1) (22,8) (2,0) (28,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1189",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,16) (1,25) (8,12) (22,11) (0,1) (20,11) (3,23) (24,8) (1,15) (14,10) (21,7) (2,6) (14,22) (0,2) (3,10) (13,23) (4,0) (11,7) (25,12) (4,19) (0,17) (21,18) (8,11) (3,0) (16,9) (6,0) (4,22) (7,5) (0,5) (26,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1078",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,13) (12,11) (19,11) (12,3) (24,12) (5,16) (6,19) (1,2) (22,5) (20,13) (1,0) (0,8) (9,15) (12,18) (0,23) (20,23) (21,0) (16,7) (10,15) (19,16) (14,7) (4,18) (10,17) (1,11) (20,3) (25,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1027",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,13) (2,4) (17,6) (11,18) (7,16) (1,5) (11,0) (0,23) (13,10) (2,0) (0,3) (7,25) (0,1) (20,12) (8,22) (25,4) (16,20) (5,16) (14,9) (9,15) (13,2) (22,16) (24,0) (19,15) (21,5) (25,15) (6,25) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1452",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,27) (24,5) (22,15) (17,28) (10,9) (3,2) (3,0) (29,15) (7,19) (0,24) (22,2) (1,0) (14,28) (13,9) (19,14) (6,8) (26,0) (4,11) (23,4) (18,9) (26,20) (12,16) (23,6) (16,11) (18,25) (12,13) (1,29) (0,28) (2,21) (14,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1145",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,3) (24,11) (13,0) (1,23) (10,4) (25,9) (18,21) (17,20) (15,18) (2,0) (0,4) (13,6) (6,26) (2,24) (25,6) (3,19) (15,10) (3,2) (0,1) (20,10) (21,8) (23,13) (4,3) (0,5) (18,14) (8,16) (21,7) (12,4) (14,13) (22,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1279",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,4) (24,10) (5,12) (11,18) (8,18) (26,0) (26,1) (10,20) (0,4) (12,27) (23,2) (0,1) (25,1) (7,13) (25,2) (20,26) (0,22) (1,6) (18,16) (25,19) (16,14) (17,18) (1,21) (15,4) (9,27) (7,20) (2,3) (17,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1605",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (25,21) (23,28) (9,2) (16,7) (11,15) (6,13) (12,6) (3,23) (26,11) (4,6) (22,24) (1,12) (21,26) (9,31) (25,14) (11,23) (27,11) (3,13) (22,27) (5,19) (18,9) (12,16) (30,17) (18,29) (24,19) (29,30) (0,1) (0,15) (0,20) (9,12) (27,8) (2,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph539",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,5) (24,7) (7,6) (19,18) (18,21) (26,12) (11,22) (15,24) (12,17) (24,14) (29,20) (28,8) (30,9) (4,26) (10,3) (6,10) (1,22) (19,30) (19,2) (0,6) (27,29) (7,23) (14,13) (27,16) (18,11) (17,27) (27,28) (21,25) (17,7) (24,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1604",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (22,29) (10,21) (2,31) (22,17) (25,18) (6,13) (18,21) (3,11) (9,8) (28,21) (0,5) (1,27) (19,4) (1,0) (9,27) (29,1) (21,23) (4,25) (12,18) (21,11) (18,30) (28,20) (5,11) (13,20) (0,26) (31,20) (22,16) (20,7) (1,14) (31,15) (25,8) (10,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph104",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,18) (6,13) (23,25) (7,15) (23,26) (15,17) (16,2) (9,3) (15,0) (24,20) (10,0) (1,19) (8,5) (2,19) (25,21) (13,9) (1,20) (3,0) (14,10) (8,4) (12,2) (22,3) (25,8) (11,8) (4,2) (23,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph328",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,20) (24,3) (16,24) (25,23) (14,4) (22,25) (27,21) (1,23) (12,10) (4,9) (18,22) (11,3) (17,0) (26,8) (11,28) (1,17) (4,6) (25,27) (8,13) (23,7) (20,8) (18,24) (18,15) (19,16) (5,24) (10,27) (9,13) (10,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1057",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,24) (25,15) (23,20) (3,25) (12,8) (6,24) (14,1) (15,8) (15,2) (24,9) (24,19) (13,23) (0,8) (0,2) (1,0) (25,13) (21,4) (17,18) (7,2) (15,18) (18,5) (11,10) (0,22) (23,6) (4,16) (11,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph134",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,23) (26,17) (26,4) (20,12) (22,8) (5,16) (0,25) (11,0) (22,5) (13,10) (15,9) (25,6) (18,11) (16,21) (19,6) (13,3) (9,14) (13,2) (0,24) (5,1) (25,7) (20,15) (4,2) (13,18) (7,16) (25,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1591",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,2) (13,2) (26,16) (4,25) (16,7) (0,1) (18,13) (0,27) (0,28) (4,0) (15,9) (12,20) (23,5) (0,3) (24,25) (9,14) (22,8) (21,30) (0,11) (13,10) (15,20) (5,16) (24,30) (26,17) (11,29) (25,7) (18,29) (6,19) (16,22) (25,15) (0,2) (1,5) (6,25) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph627",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (18,4) (8,11) (8,21) (0,28) (14,23) (1,26) (24,29) (24,13) (9,1) (25,0) (27,4) (28,23) (16,26) (21,14) (29,14) (22,6) (17,22) (16,17) (19,10) (9,19) (2,4) (20,1) (30,15) (3,11) (20,5) (23,31) (23,7) (22,31) (18,5) (22,15) (14,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph446",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,18) (18,14) (20,29) (12,18) (9,13) (25,14) (18,10) (16,20) (21,1) (27,26) (8,15) (2,17) (11,22) (21,20) (0,6) (28,15) (8,11) (26,9) (23,4) (6,15) (1,4) (9,8) (17,23) (3,22) (25,24) (11,2) (2,5) (21,7) (19,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1184",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (12,24) (9,10) (0,1) (12,14) (16,22) (6,7) (10,14) (10,20) (19,0) (3,5) (1,15) (2,22) (25,5) (17,25) (8,10) (25,6) (11,2) (0,16) (11,15) (17,4) (23,11) (0,20) (9,13) (22,18) (10,5) (21,15) (26,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph867",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (33,20) (3,2) (16,22) (17,6) (4,1) (18,7) (23,21) (9,3) (12,31) (30,8) (7,0) (14,16) (2,11) (22,20) (18,28) (0,25) (19,5) (17,8) (29,4) (24,30) (4,26) (19,2) (32,16) (26,10) (17,9) (1,21) (20,11) (26,9) (4,27) (31,13) (19,7) (13,27) (5,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1724",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (21,32) (11,20) (2,7) (12,25) (12,6) (26,16) (12,15) (18,29) (9,31) (19,16) (10,28) (4,0) (19,13) (1,0) (12,31) (7,27) (23,29) (16,0) (15,5) (1,11) (18,22) (12,30) (30,17) (3,0) (10,15) (13,31) (32,23) (2,0) (7,20) (15,11) (31,8) (11,14) (3,28) (21,4) (16,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph598",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,30) (7,23) (7,16) (6,0) (9,28) (11,24) (25,0) (5,13) (12,19) (26,2) (15,20) (13,15) (22,11) (15,26) (22,29) (4,2) (7,17) (19,11) (21,4) (22,18) (19,26) (5,14) (8,14) (27,22) (4,1) (9,5) (11,10) (23,15) (6,3) (3,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1015",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,5) (9,2) (3,20) (21,24) (5,17) (14,9) (8,6) (21,20) (14,15) (13,9) (1,0) (23,16) (13,25) (20,2) (8,20) (10,22) (10,21) (18,0) (16,15) (2,0) (16,12) (19,18) (4,7) (17,11) (19,16) (1,5) (7,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph973",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,34) (25,34) (31,16) (11,31) (6,7) (6,27) (28,15) (33,32) (4,3) (17,21) (20,19) (24,2) (8,29) (14,22) (13,7) (13,0) (32,18) (22,4) (17,23) (19,16) (3,11) (7,1) (18,13) (9,2) (23,29) (9,26) (34,27) (4,1) (28,6) (23,24) (5,10) (12,19) (30,33) (5,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1707",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,30) (28,24) (0,27) (3,5) (26,2) (1,9) (27,28) (7,32) (21,3) (10,7) (9,22) (0,3) (23,10) (15,27) (21,6) (5,11) (15,17) (25,23) (9,7) (0,2) (8,1) (12,30) (16,19) (7,14) (32,13) (4,29) (24,8) (20,28) (21,16) (6,29) (22,31) (12,11) (30,2) (0,1) (0,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1166",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,9) (7,0) (25,4) (17,21) (0,2) (6,9) (13,2) (26,12) (10,25) (14,11) (13,23) (7,12) (16,25) (4,0) (22,18) (8,21) (24,23) (1,16) (17,19) (8,13) (5,9) (10,20) (0,3) (16,8) (20,26) (22,3) (5,24) (22,15) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph938",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,4) (17,19) (24,11) (25,6) (33,6) (25,32) (8,1) (14,0) (1,11) (27,16) (13,25) (6,28) (5,16) (13,3) (29,27) (26,23) (19,32) (22,31) (12,34) (7,24) (4,17) (16,20) (27,30) (15,16) (4,29) (0,2) (18,1) (9,12) (21,22) (14,10) (23,0) (2,12) (0,20) (22,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1210",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,7) (23,8) (8,1) (24,27) (22,16) (1,0) (12,15) (11,13) (25,24) (6,16) (11,17) (2,18) (0,2) (16,12) (0,13) (26,0) (5,20) (0,4) (10,15) (4,3) (18,9) (21,9) (19,18) (14,3) (6,14) (0,3) (5,14) (13,8) (2,15) (27,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1897",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,22) (32,11) (32,17) (14,17) (2,7) (30,11) (4,6) (33,31) (8,20) (13,21) (11,5) (26,19) (1,26) (0,1) (24,12) (12,0) (28,8) (18,29) (6,26) (26,20) (29,15) (9,25) (4,15) (23,10) (9,13) (8,10) (28,14) (27,1) (33,0) (12,8) (7,14) (8,16) (25,12) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph669",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (9,18) (28,3) (22,0) (18,6) (1,3) (0,6) (10,4) (19,23) (21,8) (7,8) (26,21) (20,5) (31,6) (31,30) (4,30) (23,25) (21,10) (2,21) (16,13) (1,15) (17,23) (1,23) (11,9) (3,14) (24,0) (16,17) (12,27) (5,10) (20,15) (21,29) (31,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1594",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,24) (8,2) (29,26) (6,18) (19,6) (26,15) (9,25) (30,11) (16,21) (0,25) (16,11) (8,12) (13,4) (20,8) (28,29) (6,16) (10,3) (19,7) (22,16) (19,1) (24,17) (26,0) (2,6) (26,14) (4,11) (27,22) (0,1) (14,24) (1,23) (16,5) (0,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1849",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (4,0) (30,21) (10,2) (27,24) (30,17) (26,9) (30,15) (0,1) (1,17) (25,28) (2,0) (12,20) (8,28) (0,3) (0,32) (12,30) (23,6) (22,25) (16,14) (24,31) (14,9) (7,30) (25,27) (0,13) (11,4) (33,23) (1,19) (23,8) (29,14) (3,15) (10,4) (16,18) (33,9) (30,24) (2,19) (5,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1467",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,17) (27,16) (16,14) (16,24) (5,13) (2,4) (17,11) (9,25) (1,0) (26,21) (10,22) (13,23) (10,1) (29,16) (6,7) (17,28) (6,18) (3,15) (17,0) (21,3) (9,12) (5,4) (15,20) (3,0) (4,25) (19,22) (24,22) (27,17) (24,6) (2,0) (20,7) (27,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph234",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (27,7) (21,18) (22,24) (20,1) (16,7) (26,19) (11,2) (21,1) (15,1) (5,13) (24,10) (3,10) (25,13) (11,17) (8,25) (16,17) (6,3) (8,4) (14,4) (27,9) (20,17) (2,0) (1,23) (19,9) (16,12) (24,23) (14,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1561",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,1) (28,1) (7,4) (25,22) (4,10) (11,21) (23,17) (0,15) (8,24) (4,0) (0,1) (30,18) (3,19) (6,13) (7,17) (13,16) (1,4) (15,4) (4,24) (2,0) (4,26) (3,17) (30,6) (23,27) (23,14) (1,21) (22,24) (3,0) (21,29) (5,3) (12,9) (14,16) (20,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1785",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (5,21) (22,13) (31,10) (27,5) (24,0) (11,24) (19,21) (28,2) (30,28) (12,13) (17,26) (24,2) (0,2) (6,16) (31,23) (25,28) (1,8) (19,7) (14,28) (6,9) (3,12) (18,26) (30,8) (32,0) (17,16) (3,31) (24,20) (29,9) (17,23) (21,18) (0,17) (1,0) (14,15) (4,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1413",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,22) (3,0) (25,18) (22,2) (5,3) (10,20) (25,12) (0,1) (27,0) (2,11) (9,10) (11,15) (2,0) (0,28) (2,20) (8,29) (9,17) (28,16) (1,15) (5,26) (12,14) (6,7) (10,13) (10,14) (24,11) (6,25) (0,21) (19,22) (5,10) (20,29) (4,17) (15,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1602",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,28) (2,0) (23,25) (0,3) (9,18) (8,7) (26,21) (4,10) (1,3) (5,20) (6,0) (31,27) (29,21) (19,23) (6,18) (14,3) (0,22) (10,5) (10,21) (17,16) (12,27) (16,13) (21,2) (1,0) (30,4) (15,20) (11,9) (23,1) (0,4) (15,1) (24,0) (6,31) (17,23) (31,30) (21,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1843",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,17) (29,24) (1,6) (16,26) (16,21) (28,12) (1,0) (4,30) (8,12) (4,6) (22,11) (27,33) (22,20) (33,13) (2,33) (19,1) (7,29) (20,25) (7,12) (27,6) (6,17) (14,18) (12,31) (3,7) (6,18) (32,5) (0,2) (10,25) (26,32) (1,26) (20,19) (4,24) (9,15) (9,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1442",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,9) (11,4) (1,0) (17,27) (22,6) (22,15) (19,0) (20,14) (6,7) (2,0) (29,20) (28,26) (12,20) (1,7) (17,15) (15,23) (10,29) (18,3) (17,5) (26,21) (17,8) (17,26) (12,15) (2,19) (2,18) (8,24) (29,0) (16,18) (15,13) (19,11) (7,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1361",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,20) (27,20) (1,7) (6,22) (17,24) (6,7) (27,28) (10,19) (8,21) (3,18) (11,15) (14,18) (15,19) (11,4) (9,4) (17,5) (2,19) (8,17) (23,7) (12,15) (0,1) (12,20) (0,26) (15,22) (18,0) (25,26) (15,17) (2,16) (17,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph428",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,4) (15,22) (2,3) (6,24) (21,20) (14,20) (6,0) (29,3) (24,14) (12,5) (1,3) (13,22) (9,4) (16,5) (8,23) (6,19) (23,6) (26,5) (7,17) (13,0) (2,7) (7,13) (19,4) (28,6) (26,4) (19,11) (25,4) (17,10) (27,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph497",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,3) (18,3) (27,28) (27,3) (18,9) (27,19) (12,27) (14,9) (23,26) (1,15) (18,21) (25,18) (26,10) (21,23) (0,11) (24,4) (20,16) (6,29) (20,24) (5,29) (22,8) (2,12) (1,8) (0,6) (29,26) (15,17) (9,1) (26,7) (13,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1768",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,29) (0,1) (27,28) (3,16) (15,25) (31,30) (32,18) (26,22) (0,17) (27,11) (26,1) (4,14) (26,24) (6,32) (21,7) (16,23) (11,9) (11,3) (1,7) (12,19) (31,27) (12,5) (28,20) (25,1) (18,22) (12,16) (8,30) (0,2) (7,2) (31,4) (17,32) (19,13) (22,29) (5,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph225",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,24) (0,14) (7,21) (0,25) (27,10) (17,9) (10,23) (5,6) (9,15) (22,13) (26,21) (11,18) (12,27) (18,0) (18,20) (14,4) (12,8) (8,16) (23,17) (1,12) (7,3) (5,12) (23,4) (24,7) (24,19) (2,10) (26,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1427",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,28) (19,5) (10,3) (2,21) (14,28) (5,25) (20,15) (12,7) (1,3) (8,6) (13,15) (6,26) (28,22) (16,10) (23,8) (27,29) (9,14) (17,20) (27,5) (21,24) (24,25) (14,4) (5,0) (10,11) (7,6) (9,15) (15,18) (16,21) (2,0) (3,22) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1683",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (7,31) (15,27) (13,29) (22,24) (5,8) (11,18) (17,21) (9,11) (7,28) (15,25) (18,1) (26,4) (23,19) (6,3) (21,2) (5,0) (1,3) (10,0) (17,14) (0,1) (25,22) (4,17) (18,13) (31,0) (30,20) (11,31) (12,15) (16,27) (25,10) (23,31) (24,26) (20,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph976",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,18) (24,9) (13,26) (23,25) (32,12) (16,2) (7,5) (29,26) (14,20) (9,11) (34,14) (30,0) (34,19) (7,6) (34,13) (5,30) (4,0) (21,33) (27,28) (13,12) (3,2) (7,1) (8,3) (21,31) (8,17) (1,25) (25,21) (28,33) (9,2) (10,25) (15,23) (8,14) (13,15) (8,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1336",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,2) (7,23) (24,15) (11,10) (7,13) (24,21) (25,4) (0,2) (0,15) (11,3) (7,6) (3,26) (12,28) (22,10) (27,26) (27,1) (9,20) (0,1) (8,5) (2,6) (4,11) (16,15) (17,20) (21,17) (28,2) (18,10) (17,2) (8,11) (7,10) (22,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph215",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,11) (17,20) (6,14) (22,23) (18,25) (22,26) (3,20) (27,6) (2,4) (22,8) (24,19) (25,24) (27,2) (5,3) (26,13) (19,7) (9,12) (25,16) (15,8) (17,10) (12,0) (6,21) (1,15) (14,13) (20,24) (0,6) (4,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1006",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,0) (22,3) (18,12) (14,8) (24,17) (4,0) (22,5) (9,24) (15,5) (13,16) (1,21) (10,6) (6,20) (13,11) (3,17) (1,0) (2,23) (0,2) (23,14) (16,25) (1,8) (7,14) (21,20) (23,12) (19,11) (14,4) (2,3) (25,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1778",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,11) (16,28) (7,12) (31,18) (0,2) (0,31) (15,22) (8,6) (29,4) (1,0) (25,6) (30,13) (18,19) (19,11) (0,26) (24,23) (2,11) (13,27) (12,10) (20,16) (1,12) (17,18) (5,13) (26,21) (25,14) (18,22) (9,2) (6,3) (28,4) (28,24) (2,30) (19,8) (28,12) (23,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph937",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (11,29) (0,34) (24,13) (20,25) (16,24) (1,25) (20,30) (11,21) (33,32) (0,17) (25,2) (10,15) (18,33) (5,8) (28,12) (5,33) (2,17) (8,14) (24,3) (16,15) (29,9) (13,9) (6,11) (19,34) (27,31) (14,7) (21,5) (31,23) (30,5) (12,4) (12,26) (13,26) (22,5) (23,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1116",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,23) (2,5) (8,20) (26,6) (16,14) (0,2) (19,21) (25,24) (25,11) (25,6) (26,14) (21,4) (14,17) (5,0) (18,1) (22,11) (14,10) (1,0) (5,9) (0,3) (19,26) (23,13) (5,12) (21,3) (14,18) (6,15) (7,6) (0,4) (25,12) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph748",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,10) (12,26) (3,5) (3,32) (0,15) (17,14) (0,27) (20,28) (14,29) (8,16) (7,2) (24,2) (25,28) (10,28) (17,1) (11,19) (30,10) (10,4) (22,11) (0,21) (26,31) (24,23) (9,23) (7,26) (30,6) (2,22) (31,17) (2,13) (15,4) (32,24) (30,31) (18,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph115",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,20) (8,17) (3,10) (10,25) (0,1) (23,11) (24,8) (5,7) (19,5) (21,23) (25,6) (2,18) (25,15) (22,20) (2,17) (20,16) (0,14) (13,26) (16,0) (18,13) (11,17) (9,2) (12,9) (26,15) (4,1) (7,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1087",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,6) (12,1) (13,3) (3,22) (0,5) (7,9) (25,16) (6,0) (0,2) (1,9) (18,20) (1,8) (23,6) (2,12) (18,3) (21,23) (19,24) (20,10) (21,18) (18,9) (17,13) (15,11) (24,4) (15,8) (25,19) (14,24) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph678",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,10) (19,20) (23,2) (5,29) (26,20) (6,5) (0,1) (3,14) (16,30) (5,19) (6,7) (19,16) (18,31) (6,31) (7,11) (15,1) (5,27) (24,17) (29,9) (22,19) (12,2) (31,0) (28,2) (10,24) (13,1) (14,8) (12,5) (4,5) (8,19) (25,23) (21,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1238",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (11,15) (2,10) (15,3) (2,0) (27,0) (19,24) (4,1) (15,0) (17,14) (26,23) (13,19) (27,5) (3,6) (0,1) (3,8) (24,16) (6,22) (13,12) (25,7) (8,2) (21,25) (14,15) (0,24) (9,24) (18,4) (12,20) (12,25) (0,3) (20,18) (24,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1783",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,1) (7,32) (1,0) (0,4) (22,15) (3,7) (13,6) (1,20) (12,13) (25,11) (20,9) (24,5) (2,14) (5,16) (17,25) (10,3) (1,2) (8,32) (16,21) (23,4) (15,30) (29,28) (0,2) (32,22) (22,21) (10,18) (31,20) (19,26) (27,30) (20,28) (23,20) (0,26) (21,6) (30,0) (0,3) (17,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph897",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,28) (30,14) (23,2) (5,33) (7,26) (2,24) (0,28) (5,24) (15,0) (30,9) (7,2) (18,8) (1,17) (8,10) (10,30) (3,32) (15,4) (17,31) (11,20) (27,28) (11,22) (26,13) (26,31) (29,10) (3,6) (31,32) (19,26) (17,14) (22,0) (2,16) (25,24) (23,12) (4,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph161",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (12,20) (9,14) (25,15) (0,11) (13,3) (16,7) (13,10) (6,25) (9,15) (0,25) (11,18) (13,18) (19,6) (1,5) (2,13) (8,22) (7,25) (21,16) (16,5) (26,17) (20,15) (0,24) (16,23) (2,4) (4,26) (5,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1941",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (29,9) (19,6) (16,25) (32,5) (30,21) (28,30) (32,17) (2,16) (19,11) (1,0) (31,4) (26,34) (22,27) (20,13) (14,22) (20,27) (10,25) (26,1) (30,13) (34,16) (18,24) (7,31) (33,28) (8,23) (3,2) (8,6) (4,21) (24,0) (13,15) (30,12) (6,22) (19,9) (8,18) (33,16) (32,6) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph537",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,6) (18,28) (4,1) (15,8) (9,13) (21,20) (16,20) (11,22) (30,29) (4,23) (11,8) (5,2) (18,12) (9,8) (21,1) (28,19) (28,15) (2,11) (22,3) (2,17) (6,0) (18,10) (24,25) (25,14) (17,23) (30,20) (27,26) (7,21) (9,26) (18,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1326",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,6) (3,0) (20,2) (7,26) (1,0) (1,24) (14,28) (11,16) (8,14) (6,23) (19,7) (22,15) (12,13) (26,17) (9,13) (22,2) (24,18) (11,4) (27,0) (28,10) (14,19) (4,23) (9,18) (15,28) (12,16) (0,25) (2,3) (5,9) (0,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph362",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,6) (27,7) (4,13) (23,5) (6,22) (20,25) (27,3) (6,27) (11,4) (11,9) (9,17) (28,20) (24,2) (18,1) (15,0) (14,4) (1,13) (2,26) (17,25) (26,1) (8,14) (12,16) (2,10) (6,15) (20,19) (5,9) (15,25) (1,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph356",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (12,14) (20,24) (6,9) (28,4) (14,3) (27,4) (21,11) (23,12) (23,25) (6,18) (27,21) (26,27) (9,26) (19,1) (7,21) (5,9) (21,17) (19,23) (26,2) (14,0) (15,2) (16,2) (15,8) (9,20) (13,2) (2,22) (1,7) (8,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1235",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,20) (3,0) (17,15) (11,14) (8,22) (7,5) (1,0) (16,18) (13,11) (13,10) (2,8) (17,22) (0,5) (19,26) (7,12) (11,21) (11,0) (7,25) (18,0) (1,19) (26,23) (9,27) (3,12) (12,1) (5,16) (24,17) (4,27) (12,24) (2,0) (0,4) (6,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1829",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,28) (21,33) (5,21) (23,32) (0,1) (1,8) (7,19) (17,26) (0,3) (9,6) (33,0) (28,31) (9,30) (6,16) (24,2) (24,20) (14,15) (28,2) (24,0) (19,21) (17,23) (18,29) (11,24) (13,22) (17,0) (27,5) (28,4) (14,28) (3,12) (17,16) (2,0) (31,10) (12,13) (3,31) (30,8) (0,4) (26,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph716",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,4) (30,13) (6,19) (8,18) (22,14) (2,3) (23,8) (25,10) (32,16) (30,12) (9,26) (24,0) (20,13) (4,29) (19,11) (5,32) (19,9) (6,8) (6,31) (7,31) (32,17) (1,26) (20,27) (25,16) (28,30) (16,2) (30,21) (24,18) (6,22) (13,15) (22,27) (16,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1955",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,22) (25,10) (0,24) (12,30) (0,26) (8,32) (14,18) (17,31) (2,21) (33,12) (2,31) (13,34) (26,7) (0,3) (3,30) (11,32) (34,12) (21,19) (20,2) (6,22) (0,1) (12,16) (10,29) (23,22) (3,9) (32,17) (15,4) (13,8) (11,25) (18,25) (12,27) (4,31) (28,34) (23,0) (5,2) (19,24) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1341",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,18) (13,23) (14,5) (0,9) (0,19) (22,15) (7,8) (6,4) (12,14) (26,2) (1,0) (0,3) (8,1) (7,4) (28,25) (24,11) (10,1) (2,0) (11,25) (5,19) (3,16) (3,23) (22,28) (21,17) (20,28) (2,7) (23,21) (10,19) (27,28) (17,5) (13,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1404",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,0) (8,25) (5,8) (26,20) (28,23) (6,13) (9,18) (4,2) (10,14) (3,9) (25,28) (4,8) (2,12) (23,29) (19,2) (0,10) (1,28) (17,15) (2,16) (11,8) (25,21) (27,19) (20,1) (2,0) (15,0) (9,13) (1,0) (22,3) (7,15) (27,9) (23,24) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1496",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,2) (21,25) (15,0) (9,24) (14,15) (19,13) (6,23) (25,28) (0,22) (20,18) (4,18) (0,1) (4,1) (20,12) (2,10) (28,24) (15,11) (17,14) (27,26) (0,24) (24,19) (6,3) (5,27) (16,24) (3,15) (13,12) (2,0) (3,8) (7,25) (29,22) (26,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1230",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,24) (2,0) (0,27) (19,3) (24,5) (4,24) (8,25) (13,7) (2,12) (20,12) (22,9) (27,17) (14,15) (18,6) (12,25) (11,15) (9,26) (25,19) (4,9) (26,21) (6,16) (11,18) (23,15) (0,1) (16,13) (17,8) (4,16) (10,1) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph666",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,28) (26,27) (10,29) (6,1) (30,6) (27,11) (4,16) (23,31) (22,5) (10,2) (4,3) (26,21) (9,12) (18,26) (14,28) (28,12) (25,22) (9,19) (13,29) (9,20) (24,4) (18,9) (0,2) (19,13) (23,16) (6,13) (26,8) (25,4) (6,24) (15,20) (20,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1044",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,15) (20,12) (14,2) (0,1) (9,19) (7,11) (0,12) (19,2) (16,21) (15,24) (1,12) (6,13) (2,17) (2,0) (7,4) (19,25) (8,18) (23,19) (3,6) (12,16) (13,23) (22,21) (5,7) (23,8) (5,10) (22,17) (4,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph995",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,32) (24,17) (12,33) (16,13) (17,25) (32,11) (34,29) (2,16) (29,15) (11,22) (15,4) (28,1) (21,20) (30,10) (2,30) (0,3) (14,25) (23,19) (0,30) (19,22) (14,9) (16,31) (23,28) (27,7) (12,1) (23,21) (10,28) (18,33) (34,3) (8,15) (25,0) (24,26) (1,7) (6,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph838",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,2) (24,14) (27,6) (10,26) (0,33) (22,29) (29,5) (7,31) (17,7) (32,8) (17,15) (30,27) (16,8) (3,25) (15,21) (25,1) (18,5) (19,33) (1,9) (3,13) (8,19) (20,0) (4,24) (1,23) (31,19) (12,16) (17,6) (4,25) (1,15) (22,4) (25,28) (13,11) (10,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph214",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,5) (22,24) (8,27) (23,1) (16,17) (7,1) (6,7) (23,14) (20,2) (7,16) (12,0) (4,2) (17,12) (25,24) (2,0) (3,8) (9,10) (26,3) (9,21) (12,18) (17,11) (13,3) (26,5) (4,15) (19,15) (8,11) (9,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph926",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,11) (30,5) (6,2) (21,17) (34,27) (26,23) (1,29) (4,11) (7,25) (15,34) (13,18) (5,9) (13,25) (8,27) (25,31) (12,33) (12,26) (12,17) (28,24) (9,22) (29,25) (7,10) (1,28) (14,34) (4,0) (8,18) (32,0) (13,20) (2,16) (30,3) (1,5) (5,12) (14,16) (1,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1190",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,0) (6,16) (26,11) (18,8) (2,0) (23,0) (16,20) (26,0) (21,1) (26,14) (8,2) (3,10) (24,15) (16,5) (6,17) (1,19) (25,9) (26,4) (12,8) (6,19) (16,11) (2,6) (16,22) (19,7) (25,14) (24,22) (1,0) (13,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph679",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,15) (16,8) (5,4) (16,17) (30,16) (25,15) (12,4) (30,1) (10,12) (17,2) (31,6) (23,20) (22,0) (24,11) (22,28) (9,6) (27,26) (16,19) (4,13) (9,14) (8,21) (26,3) (31,15) (4,29) (3,28) (23,25) (18,7) (18,21) (14,21) (27,5) (30,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1846",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,30) (27,20) (19,11) (2,3) (22,14) (8,6) (28,30) (7,31) (25,10) (28,33) (5,32) (9,19) (18,8) (17,32) (27,22) (13,15) (2,0) (16,33) (9,26) (32,16) (4,29) (21,4) (0,1) (6,22) (13,30) (23,8) (0,24) (26,1) (2,16) (30,12) (13,20) (18,24) (31,6) (16,25) (19,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1355",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,14) (28,4) (27,23) (19,25) (11,7) (10,26) (16,12) (16,1) (21,4) (7,9) (0,19) (14,20) (26,24) (23,11) (17,13) (1,0) (5,18) (22,24) (8,17) (15,26) (14,21) (4,5) (15,12) (9,10) (6,10) (2,26) (28,0) (21,9) (0,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph994",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,31) (4,30) (34,4) (9,23) (15,28) (6,4) (13,2) (6,8) (25,16) (8,29) (4,1) (6,11) (2,1) (19,11) (15,34) (0,12) (1,3) (28,21) (12,27) (11,12) (14,17) (30,22) (19,24) (34,33) (26,34) (34,32) (7,23) (23,17) (1,18) (27,5) (7,20) (15,20) (16,26) (3,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph78",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,21) (23,2) (7,14) (9,24) (4,0) (12,18) (17,24) (3,22) (12,23) (5,22) (6,20) (11,13) (8,14) (17,3) (6,10) (14,23) (25,10) (15,5) (21,20) (4,14) (11,19) (1,8) (13,16) (3,2) (16,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph310",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,18) (23,21) (25,24) (27,22) (2,22) (24,20) (7,13) (7,18) (8,15) (1,14) (9,16) (15,13) (24,27) (10,14) (23,0) (28,3) (16,19) (10,21) (3,25) (14,17) (3,12) (26,11) (6,26) (4,23) (20,17) (8,23) (11,5) (5,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1874",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,16) (2,20) (12,26) (14,28) (10,27) (14,25) (6,21) (13,23) (1,4) (14,15) (5,18) (1,0) (1,30) (24,33) (14,26) (29,32) (13,9) (11,15) (6,8) (3,7) (9,17) (0,10) (6,5) (1,12) (28,17) (1,2) (5,22) (24,5) (13,21) (7,17) (17,32) (27,21) (27,19) (31,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1760",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,13) (3,0) (11,1) (3,16) (6,24) (17,19) (12,0) (28,22) (29,27) (23,0) (7,1) (4,18) (4,0) (0,1) (1,18) (31,19) (21,23) (0,20) (29,4) (26,27) (2,13) (32,0) (8,12) (4,17) (16,27) (6,30) (22,27) (20,16) (25,10) (0,2) (14,22) (9,14) (25,32) (5,24) (11,15) (25,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1129",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,25) (13,9) (0,1) (20,10) (6,1) (7,23) (5,6) (19,24) (6,16) (19,13) (21,12) (25,22) (0,2) (15,0) (18,9) (15,6) (1,17) (9,11) (4,0) (26,15) (25,14) (0,3) (18,3) (8,23) (18,2) (14,8) (20,14) (12,11) (6,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph276",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,24) (1,17) (8,6) (25,17) (14,22) (7,15) (2,10) (12,13) (9,18) (10,25) (5,12) (24,27) (7,10) (11,1) (9,7) (2,23) (0,27) (7,16) (9,19) (4,14) (14,15) (26,21) (3,11) (26,9) (9,6) (0,1) (13,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1819",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,31) (27,28) (9,17) (5,15) (13,20) (31,19) (11,6) (4,0) (13,2) (12,14) (0,1) (20,10) (20,21) (32,23) (3,0) (4,19) (8,13) (12,10) (22,29) (7,24) (4,21) (18,9) (25,10) (1,7) (11,10) (33,1) (5,16) (10,16) (3,24) (28,19) (0,18) (4,33) (28,0) (0,2) (31,26) (2,23) (30,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1924",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,20) (3,1) (14,4) (6,31) (0,2) (23,27) (2,23) (9,24) (26,16) (33,23) (24,8) (11,31) (14,32) (8,29) (1,0) (10,1) (18,13) (33,10) (25,34) (32,33) (25,21) (27,9) (5,32) (17,24) (23,19) (30,32) (27,11) (22,6) (1,18) (7,20) (9,28) (8,16) (27,15) (12,30) (34,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1440",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,2) (9,13) (4,24) (14,0) (19,11) (11,5) (25,18) (18,6) (27,3) (28,21) (26,15) (24,29) (0,19) (20,0) (8,3) (12,11) (11,8) (16,26) (4,26) (7,17) (1,0) (10,9) (0,2) (12,22) (3,10) (16,18) (1,16) (2,13) (7,28) (4,28) (24,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph557",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,13) (6,24) (25,21) (30,15) (19,8) (17,19) (24,4) (6,20) (14,28) (21,3) (12,8) (10,14) (20,1) (28,23) (13,15) (13,11) (22,19) (13,18) (2,0) (3,15) (27,9) (5,3) (8,29) (30,16) (5,14) (26,5) (1,9) (3,2) (21,29) (5,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph617",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,11) (22,16) (21,10) (25,8) (28,20) (22,29) (1,27) (18,21) (22,17) (21,28) (31,15) (27,9) (5,11) (29,1) (7,20) (19,4) (30,18) (23,21) (31,20) (20,13) (10,24) (4,25) (13,6) (5,0) (31,2) (0,26) (18,25) (11,3) (8,9) (12,18) (14,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph314",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,23) (2,15) (1,11) (9,24) (0,28) (6,13) (7,0) (18,8) (19,9) (14,0) (7,20) (26,10) (15,13) (9,25) (16,21) (22,17) (10,21) (13,27) (21,4) (20,22) (9,5) (3,15) (27,26) (8,7) (14,12) (0,9) (4,23) (11,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph584",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,18) (13,15) (26,5) (8,12) (17,19) (28,23) (27,9) (21,25) (1,5) (19,8) (7,13) (1,20) (6,24) (2,3) (30,16) (14,5) (28,14) (19,22) (21,3) (15,30) (29,21) (24,4) (9,1) (3,15) (11,13) (8,29) (3,5) (10,14) (0,2) (6,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1165",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,14) (8,20) (17,2) (5,11) (7,6) (20,7) (10,11) (3,11) (0,15) (10,7) (24,26) (15,10) (15,13) (3,0) (25,3) (26,2) (21,22) (17,18) (12,22) (2,0) (2,16) (21,17) (23,4) (2,6) (9,7) (1,8) (4,11) (19,10) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1366",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,9) (20,10) (20,27) (0,3) (27,8) (22,18) (25,10) (6,9) (24,5) (28,27) (26,12) (4,0) (17,21) (0,2) (1,16) (23,13) (26,16) (7,12) (17,19) (11,9) (25,4) (1,0) (24,23) (13,2) (0,7) (0,5) (11,14) (3,22) (21,8) (15,22) (8,13) (25,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph659",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,23) (18,30) (24,11) (5,7) (20,3) (31,12) (1,17) (22,18) (26,12) (0,9) (5,4) (24,27) (30,16) (28,16) (0,17) (14,13) (21,11) (19,7) (30,4) (11,25) (2,16) (12,5) (8,15) (20,7) (15,9) (1,31) (13,29) (12,14) (12,10) (12,6) (21,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1665",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,2) (5,24) (0,3) (23,4) (13,12) (16,21) (20,9) (0,1) (20,29) (0,2) (20,22) (6,13) (0,8) (25,17) (22,21) (11,25) (20,23) (0,30) (3,10) (28,31) (1,10) (14,2) (22,15) (19,26) (15,30) (6,21) (30,26) (20,1) (28,7) (28,27) (18,10) (17,8) (5,16) (3,7) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph274",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (19,16) (26,1) (24,3) (23,9) (20,27) (25,6) (25,8) (22,2) (20,6) (10,17) (0,19) (23,18) (6,19) (16,7) (4,17) (18,1) (12,27) (15,0) (14,15) (23,16) (5,17) (20,2) (4,13) (24,8) (4,25) (25,11) (21,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1985",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,31) (27,20) (13,15) (9,19) (24,0) (22,6) (6,32) (22,27) (5,32) (30,12) (13,20) (30,21) (23,8) (1,26) (21,4) (33,28) (1,0) (14,22) (30,13) (2,3) (18,24) (28,30) (8,18) (6,8) (26,34) (16,25) (19,11) (16,2) (29,9) (19,6) (10,25) (16,33) (34,16) (17,32) (31,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1678",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,25) (31,8) (1,29) (14,12) (27,5) (9,5) (9,21) (18,13) (12,5) (1,15) (25,13) (2,0) (19,13) (18,8) (4,0) (16,14) (28,25) (1,5) (17,20) (0,30) (6,2) (0,1) (7,10) (12,24) (26,1) (16,2) (11,4) (12,17) (7,25) (26,22) (23,28) (6,11) (3,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1265",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (9,16) (12,17) (5,4) (26,13) (20,25) (11,16) (7,2) (22,25) (7,0) (5,11) (15,27) (0,1) (10,15) (1,19) (3,8) (1,6) (0,14) (20,0) (14,12) (23,13) (14,11) (5,24) (1,17) (26,1) (13,18) (23,8) (2,27) (4,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph246",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,18) (3,22) (4,8) (22,26) (2,26) (2,23) (8,10) (7,15) (20,23) (16,8) (11,26) (24,12) (14,2) (6,9) (8,11) (9,13) (0,20) (7,5) (17,10) (5,12) (15,1) (19,26) (21,17) (15,26) (6,2) (27,18) (7,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1545",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,28) (25,14) (6,28) (17,1) (9,12) (13,22) (20,0) (15,27) (2,12) (29,18) (2,15) (4,10) (18,6) (25,7) (20,23) (0,1) (7,3) (15,24) (12,26) (21,16) (14,12) (12,22) (2,1) (8,30) (14,0) (30,15) (19,4) (16,6) (11,6) (11,5) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph62",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,4) (21,18) (11,24) (8,16) (14,18) (23,1) (18,15) (20,17) (15,10) (22,5) (24,2) (6,13) (21,7) (4,12) (23,13) (13,14) (9,25) (0,13) (0,5) (6,25) (21,8) (3,2) (10,20) (4,10) (19,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph48",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,11) (18,13) (19,0) (6,7) (20,5) (17,2) (23,18) (2,24) (7,14) (8,7) (16,7) (4,15) (13,1) (9,3) (0,25) (12,8) (21,3) (19,16) (20,3) (0,1) (17,22) (21,23) (4,23) (10,0) (6,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1563",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,10) (11,2) (9,22) (7,20) (14,20) (9,2) (11,6) (2,0) (25,11) (27,18) (0,1) (27,3) (13,17) (29,19) (7,25) (4,17) (10,29) (8,19) (12,13) (27,14) (16,29) (2,5) (16,23) (15,2) (13,30) (19,21) (3,1) (0,28) (26,12) (17,19) (11,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1671",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,14) (3,21) (27,1) (2,0) (21,11) (0,1) (1,28) (22,20) (21,29) (2,29) (27,22) (17,18) (30,6) (4,0) (18,31) (24,11) (24,5) (0,20) (24,14) (12,10) (22,18) (8,4) (4,13) (16,0) (25,19) (30,15) (9,10) (19,13) (0,3) (8,26) (28,14) (11,19) (28,15) (7,1) (9,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1533",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,12) (0,1) (8,11) (9,21) (7,13) (27,23) (2,0) (17,20) (6,21) (4,1) (29,14) (30,19) (14,2) (4,22) (30,15) (8,28) (19,6) (14,26) (16,0) (0,3) (5,28) (26,0) (24,11) (16,10) (18,21) (1,20) (23,4) (28,16) (28,23) (20,6) (18,3) (25,24) (9,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph960",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,22) (29,25) (10,23) (21,9) (31,34) (13,14) (1,26) (18,5) (14,23) (15,22) (6,22) (8,12) (3,11) (29,20) (32,5) (28,0) (28,4) (27,0) (19,11) (7,34) (30,23) (4,18) (8,21) (17,22) (14,32) (4,2) (33,15) (1,20) (31,23) (1,9) (24,14) (19,24) (17,16) (26,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph190",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,0) (8,14) (6,5) (22,15) (20,24) (4,18) (26,0) (23,7) (9,21) (8,23) (12,17) (24,21) (12,15) (3,10) (21,6) (22,6) (7,25) (19,12) (13,1) (20,4) (26,23) (11,23) (2,26) (13,16) (9,3) (20,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1986",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,27) (2,13) (29,1) (5,20) (24,34) (29,28) (32,2) (7,27) (30,14) (32,8) (18,6) (9,12) (4,34) (4,3) (12,30) (26,1) (0,28) (20,6) (1,0) (31,22) (26,17) (12,8) (17,25) (17,16) (22,23) (31,10) (29,10) (5,16) (21,31) (19,9) (1,19) (31,33) (11,29) (22,15) (19,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph138",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,4) (25,23) (25,21) (11,8) (4,2) (1,20) (3,22) (9,13) (8,5) (26,23) (16,2) (9,18) (12,2) (14,10) (7,15) (24,20) (9,3) (19,2) (0,10) (23,9) (0,3) (25,8) (13,6) (17,15) (0,15) (19,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1565",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,24) (2,20) (7,8) (7,13) (23,16) (17,8) (1,19) (23,9) (14,21) (7,27) (0,3) (30,11) (8,3) (4,22) (28,30) (16,10) (18,9) (14,9) (6,20) (0,1) (5,24) (15,8) (3,29) (19,23) (12,25) (21,2) (26,12) (22,14) (28,27) (21,27) (12,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1996",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,27) (0,1) (34,3) (23,18) (15,31) (14,1) (19,5) (7,9) (26,29) (17,24) (19,11) (25,34) (6,11) (27,0) (12,27) (13,22) (28,1) (8,5) (19,30) (2,26) (13,2) (19,20) (4,23) (32,29) (10,29) (0,31) (22,27) (33,22) (23,34) (27,1) (17,7) (2,0) (17,4) (17,30) (8,16) (16,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1745",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,14) (27,5) (0,2) (15,24) (9,6) (32,15) (19,11) (8,24) (15,6) (9,25) (4,25) (0,3) (2,23) (18,19) (31,21) (1,0) (13,26) (14,21) (4,1) (31,22) (28,20) (14,19) (3,30) (17,18) (26,24) (5,21) (26,0) (15,16) (29,21) (1,29) (28,19) (3,12) (7,29) (12,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1614",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (20,23) (28,24) (24,8) (0,1) (28,19) (31,7) (13,7) (3,21) (27,15) (21,6) (16,18) (9,7) (1,8) (0,12) (2,25) (28,27) (16,21) (11,12) (9,22) (29,12) (5,11) (29,4) (9,1) (27,0) (30,2) (7,10) (14,15) (22,30) (10,23) (0,2) (17,30) (3,5) (26,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1615",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,19) (20,13) (5,4) (30,0) (27,26) (5,16) (15,7) (21,14) (22,20) (2,0) (17,2) (12,24) (31,1) (3,0) (9,22) (15,14) (14,20) (25,21) (14,0) (23,22) (30,8) (21,4) (27,17) (27,6) (31,6) (21,10) (1,0) (4,12) (18,9) (29,27) (28,5) (23,3) (21,17) (5,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph413",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,27) (6,9) (26,27) (25,12) (18,19) (14,10) (22,7) (26,4) (24,13) (5,3) (7,6) (21,23) (20,11) (7,17) (17,27) (18,21) (12,17) (22,1) (10,3) (21,24) (24,14) (0,6) (19,29) (24,7) (29,16) (19,2) (27,28) (8,28) (11,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1461",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (27,5) (18,15) (22,28) (10,16) (28,14) (8,23) (9,14) (25,5) (3,10) (5,19) (8,6) (6,7) (21,16) (8,28) (0,2) (2,21) (15,13) (20,17) (12,7) (0,5) (20,15) (10,11) (0,1) (26,6) (3,22) (1,3) (25,24) (24,21) (9,15) (4,14) (27,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1310",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,0) (0,4) (2,19) (23,25) (10,8) (22,6) (0,28) (13,10) (0,2) (25,17) (10,5) (5,14) (16,4) (7,27) (14,27) (20,28) (27,21) (3,12) (3,14) (0,1) (11,6) (26,8) (25,16) (16,8) (3,0) (1,27) (15,3) (16,19) (9,18) (9,5) (3,11) (24,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph315",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,9) (18,8) (13,27) (8,7) (11,1) (10,26) (19,9) (7,20) (2,15) (7,11) (23,4) (4,21) (20,22) (21,10) (17,22) (24,9) (19,23) (13,15) (28,0) (0,14) (9,5) (3,15) (14,12) (25,9) (16,21) (6,13) (26,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph963",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (34,17) (24,11) (2,28) (28,14) (19,7) (32,9) (23,0) (16,17) (9,6) (21,29) (8,1) (25,28) (23,17) (0,24) (12,13) (28,33) (19,21) (31,10) (18,30) (8,30) (26,18) (12,3) (14,15) (20,24) (21,33) (31,3) (28,4) (16,6) (17,26) (27,5) (31,34) (2,24) (13,22) (5,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph252",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,3) (16,4) (16,8) (11,3) (8,25) (16,24) (27,0) (13,10) (14,23) (5,10) (1,27) (25,17) (12,3) (8,10) (9,18) (20,27) (7,27) (19,0) (6,11) (6,21) (16,19) (9,5) (2,19) (14,3) (5,14) (26,14) (25,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph565",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (16,2) (15,17) (6,13) (0,15) (15,7) (26,23) (9,13) (25,21) (9,18) (0,10) (3,22) (30,3) (27,9) (8,5) (8,25) (8,4) (8,11) (20,27) (2,12) (2,19) (23,28) (1,28) (28,25) (19,29) (14,10) (24,9) (23,30) (3,0) (20,1) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1739",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,2) (6,30) (25,26) (31,5) (23,32) (26,3) (19,30) (4,11) (17,21) (30,9) (14,5) (7,27) (27,15) (25,14) (6,16) (23,4) (20,22) (15,0) (24,0) (12,29) (20,17) (6,8) (24,23) (16,32) (9,1) (21,19) (0,1) (27,29) (10,22) (28,9) (13,23) (10,2) (31,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph405",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,2) (2,20) (22,6) (14,11) (20,12) (7,12) (10,17) (3,18) (9,5) (28,7) (9,22) (29,0) (10,16) (26,4) (19,27) (25,13) (21,22) (26,21) (14,4) (6,19) (1,3) (25,12) (21,23) (29,8) (24,10) (13,21) (4,3) (15,14) (8,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph361",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,19) (9,3) (7,2) (8,6) (10,23) (28,2) (20,6) (14,12) (13,25) (8,14) (16,4) (9,7) (27,5) (17,21) (14,16) (28,22) (20,24) (28,13) (18,16) (15,19) (0,13) (26,7) (1,9) (11,14) (10,26) (17,14) (27,17) (15,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph806",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,9) (10,31) (8,12) (1,19) (29,10) (0,28) (32,31) (7,27) (24,27) (22,31) (29,24) (18,6) (22,15) (6,20) (3,19) (9,19) (1,29) (2,32) (30,14) (28,12) (16,5) (17,25) (11,29) (3,4) (1,26) (22,23) (4,33) (8,30) (13,2) (17,26) (20,5) (31,21) (16,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph90",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,24) (9,10) (25,9) (17,18) (8,21) (10,13) (16,9) (21,0) (4,18) (1,2) (16,5) (3,20) (16,11) (8,3) (19,4) (13,22) (25,1) (23,8) (7,3) (14,16) (6,12) (24,3) (6,15) (12,11) (8,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph178",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,6) (8,23) (3,18) (5,6) (15,0) (4,6) (6,1) (16,6) (17,1) (18,2) (14,20) (13,9) (11,9) (20,10) (25,14) (25,22) (23,7) (21,12) (6,25) (13,19) (26,15) (14,8) (24,19) (9,18) (0,3) (11,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1798",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,3) (2,1) (31,28) (23,9) (16,20) (14,27) (18,8) (10,2) (1,0) (0,4) (9,17) (2,13) (5,25) (5,20) (25,6) (17,28) (26,29) (4,15) (12,9) (23,24) (3,19) (21,32) (14,21) (30,22) (14,11) (4,29) (25,30) (1,8) (7,27) (4,30) (7,29) (18,21) (9,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1658",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,27) (6,7) (10,29) (17,30) (8,5) (0,27) (27,20) (30,19) (19,9) (5,19) (27,11) (29,26) (0,1) (3,11) (31,14) (7,17) (27,1) (19,18) (21,17) (23,15) (2,13) (26,2) (17,4) (2,0) (12,1) (22,28) (22,25) (8,16) (16,10) (0,24) (31,4) (23,1) (13,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph14",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,22) (2,11) (16,11) (9,2) (13,0) (25,17) (3,1) (1,0) (19,10) (12,23) (7,25) (14,20) (24,11) (15,10) (11,6) (7,20) (4,17) (12,13) (9,21) (15,2) (17,19) (8,19) (5,2) (18,19) (3,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph784",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,16) (11,8) (11,16) (10,7) (7,3) (28,6) (29,26) (22,13) (19,28) (24,3) (17,14) (3,20) (27,23) (19,32) (14,5) (25,19) (12,11) (5,15) (26,12) (17,3) (20,21) (32,9) (4,1) (20,18) (2,15) (1,27) (30,7) (16,1) (11,22) (8,0) (31,9) (11,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph380",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,19) (5,2) (28,12) (26,15) (3,21) (27,25) (6,12) (21,14) (5,12) (18,14) (4,21) (8,22) (11,25) (14,20) (13,27) (25,6) (7,8) (2,0) (26,14) (17,23) (15,6) (14,10) (1,18) (19,23) (25,16) (6,7) (9,5) (24,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph869",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,1) (6,0) (5,4) (26,14) (25,13) (32,2) (12,21) (33,27) (29,32) (27,4) (30,16) (24,16) (24,11) (23,22) (12,15) (25,0) (21,22) (28,15) (20,27) (16,9) (30,22) (2,17) (32,10) (7,29) (15,14) (18,26) (22,3) (19,1) (31,28) (21,8) (33,15) (20,0) (23,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1126",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,21) (4,18) (14,6) (22,3) (22,19) (23,15) (21,11) (24,2) (11,3) (26,23) (14,0) (24,9) (24,8) (21,14) (16,15) (1,7) (2,0) (23,1) (17,21) (1,0) (15,8) (16,12) (20,26) (2,10) (22,10) (3,0) (8,25) (13,5) (21,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1485",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,4) (11,2) (2,0) (12,19) (13,15) (22,18) (0,6) (7,16) (22,11) (15,23) (14,5) (4,21) (8,14) (10,11) (22,28) (7,23) (11,19) (0,24) (26,15) (26,29) (3,6) (4,2) (5,13) (3,23) (25,22) (19,26) (7,17) (27,9) (1,0) (9,5) (20,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1306",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,7) (13,18) (0,10) (6,28) (19,16) (17,6) (11,23) (20,3) (2,24) (7,16) (1,0) (0,19) (1,13) (3,21) (21,23) (2,0) (22,28) (17,23) (20,5) (27,7) (9,3) (26,2) (17,0) (12,8) (2,6) (25,18) (4,15) (14,7) (4,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph647",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (25,2) (21,5) (26,12) (9,29) (21,11) (31,19) (3,24) (11,28) (6,11) (23,24) (14,7) (16,15) (4,12) (30,5) (18,5) (20,25) (14,8) (5,8) (13,24) (31,0) (20,30) (13,9) (23,27) (26,13) (29,5) (17,0) (16,24) (15,10) (2,17) (12,22) (1,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph683",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,26) (0,8) (22,13) (13,31) (17,11) (3,14) (0,13) (16,2) (15,6) (7,16) (10,24) (24,11) (10,3) (15,19) (17,25) (30,18) (9,1) (30,13) (4,8) (26,23) (8,27) (7,23) (6,21) (15,12) (5,22) (24,20) (10,4) (0,15) (29,0) (1,29) (8,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1356",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,24) (8,6) (15,20) (11,8) (4,15) (0,4) (7,16) (0,12) (5,26) (10,7) (23,18) (25,1) (1,0) (23,24) (26,3) (9,22) (9,13) (17,12) (0,2) (21,2) (4,2) (8,3) (3,0) (24,5) (1,7) (9,25) (16,17) (14,3) (11,17) (19,12) (28,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph59",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,12) (22,13) (21,25) (17,1) (0,20) (16,13) (13,5) (3,8) (7,2) (4,5) (11,14) (17,12) (10,15) (6,1) (18,1) (7,0) (19,4) (1,24) (23,8) (9,16) (25,2) (5,11) (14,0) (20,23) (11,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1970",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,2) (14,34) (29,1) (13,25) (4,0) (34,27) (27,8) (7,25) (11,4) (14,16) (11,6) (7,10) (1,0) (31,25) (5,1) (23,26) (22,9) (12,26) (12,5) (12,17) (8,18) (28,1) (3,0) (3,30) (0,32) (13,18) (29,25) (21,17) (12,33) (5,30) (5,9) (16,2) (20,13) (1,19) (34,15) (24,28) (2,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph370",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,26) (3,25) (11,8) (6,2) (13,23) (27,4) (11,22) (12,27) (1,28) (10,14) (5,7) (20,4) (7,28) (0,6) (1,0) (18,25) (24,7) (11,23) (1,15) (3,10) (16,9) (11,7) (5,16) (21,22) (21,19) (8,12) (0,17) (14,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1449",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (0,4) (15,16) (26,16) (14,0) (29,10) (17,25) (24,11) (12,14) (24,25) (27,8) (23,18) (28,25) (19,20) (18,6) (14,9) (13,14) (0,3) (27,22) (27,5) (1,27) (6,5) (9,4) (20,15) (25,19) (14,3) (2,0) (17,7) (28,29) (4,2) (3,5) (17,2) (21,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1457",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,8) (23,13) (14,11) (5,24) (19,17) (2,13) (0,24) (29,3) (16,25) (26,23) (12,7) (27,8) (9,6) (11,9) (26,12) (22,18) (21,17) (5,9) (7,0) (10,25) (8,21) (28,16) (29,27) (25,4) (22,15) (1,0) (22,3) (20,10) (16,1) (27,20) (3,0) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph433",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,9) (20,9) (2,17) (14,0) (9,4) (2,14) (29,10) (21,7) (2,24) (11,8) (22,6) (29,5) (6,9) (2,16) (21,27) (12,23) (8,15) (13,21) (15,12) (1,19) (14,3) (7,1) (26,23) (21,18) (27,28) (20,25) (2,26) (27,29) (23,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1187",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,11) (1,8) (9,18) (16,22) (3,0) (0,13) (15,10) (7,16) (0,24) (9,21) (16,6) (0,5) (5,14) (0,4) (26,17) (17,11) (2,15) (24,25) (18,19) (5,20) (15,12) (14,6) (3,4) (0,1) (8,23) (3,14) (18,2) (0,2) (16,12) (13,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph935",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,32) (5,4) (7,20) (16,2) (22,18) (24,11) (11,26) (17,0) (0,25) (5,7) (21,11) (17,1) (16,31) (18,30) (6,12) (12,34) (20,3) (32,28) (13,30) (5,12) (14,12) (31,1) (15,9) (34,16) (14,13) (29,24) (30,32) (19,7) (33,4) (10,12) (27,12) (8,15) (21,20) (23,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1771",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,12) (5,27) (29,31) (3,16) (6,4) (16,4) (14,26) (15,2) (20,26) (1,0) (12,24) (13,23) (17,8) (2,12) (5,32) (1,26) (13,31) (10,1) (0,9) (25,5) (15,13) (21,27) (10,11) (21,28) (28,19) (20,9) (6,5) (18,30) (26,22) (25,30) (20,8) (21,20) (7,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1642",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,22) (12,2) (23,25) (11,1) (23,29) (28,24) (11,31) (16,27) (15,14) (2,17) (20,30) (1,0) (13,9) (4,5) (0,5) (23,5) (10,27) (7,19) (20,11) (8,16) (29,15) (26,20) (25,18) (23,19) (10,11) (27,24) (5,3) (13,10) (14,1) (2,1) (0,2) (10,6) (0,4) (21,28) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1515",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,20) (16,0) (17,2) (2,18) (1,0) (26,15) (4,0) (21,9) (8,17) (16,20) (29,8) (17,11) (13,26) (15,30) (10,25) (22,2) (3,0) (7,8) (12,29) (10,3) (11,28) (13,20) (1,4) (0,2) (25,5) (25,19) (24,0) (27,23) (28,9) (5,7) (14,29) (6,30) (18,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph735",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,12) (5,23) (17,0) (7,23) (6,17) (20,28) (14,7) (25,32) (24,21) (19,5) (13,22) (0,15) (6,8) (12,30) (29,4) (2,9) (16,31) (18,30) (11,5) (20,27) (16,11) (13,28) (26,27) (18,32) (1,17) (17,26) (19,1) (3,12) (10,20) (9,21) (24,31) (4,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph337",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,16) (27,17) (28,21) (5,23) (25,28) (5,24) (3,2) (19,0) (18,10) (13,22) (21,10) (9,17) (26,0) (9,11) (0,14) (25,15) (2,20) (18,23) (9,24) (26,12) (20,19) (12,15) (8,4) (6,14) (15,22) (4,27) (7,1) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph5",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,11) (17,22) (10,7) (17,14) (1,2) (16,11) (23,22) (9,23) (8,5) (21,19) (0,25) (3,19) (4,12) (19,15) (20,4) (21,18) (0,20) (13,22) (22,24) (22,10) (19,4) (23,6) (11,9) (2,25) (12,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1620",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,30) (2,11) (2,3) (15,5) (4,28) (14,16) (8,29) (7,18) (17,8) (19,2) (3,0) (21,1) (26,9) (11,20) (12,31) (17,9) (4,0) (7,0) (20,16) (4,26) (13,30) (10,26) (1,4) (5,19) (16,31) (0,2) (18,25) (7,19) (27,4) (17,6) (24,0) (9,3) (22,21) (0,1) (27,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph312",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,4) (13,4) (27,17) (7,18) (9,23) (7,20) (15,5) (24,7) (11,25) (20,23) (21,10) (22,27) (1,8) (27,6) (4,5) (28,4) (27,12) (23,6) (0,9) (14,28) (2,17) (21,19) (25,5) (20,16) (8,21) (0,13) (3,9) (26,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1990",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,28) (30,34) (24,17) (23,24) (1,18) (34,13) (12,19) (33,2) (25,16) (16,32) (14,8) (25,31) (29,11) (7,6) (33,21) (11,25) (0,8) (10,7) (4,32) (32,10) (1,8) (1,0) (11,9) (2,0) (23,26) (5,17) (34,3) (20,2) (21,11) (6,12) (27,17) (23,30) (31,15) (22,12) (23,6) (5,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1979",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,3) (10,0) (0,2) (1,29) (11,6) (7,28) (23,11) (0,1) (12,2) (3,4) (28,13) (25,27) (28,6) (11,18) (1,15) (19,9) (28,25) (30,10) (4,31) (34,5) (32,21) (33,12) (16,32) (26,2) (14,34) (29,8) (17,12) (9,5) (29,20) (0,33) (12,28) (22,30) (20,28) (24,19) (33,14) (32,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph846",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,22) (31,23) (0,26) (15,28) (2,16) (20,4) (25,28) (8,7) (33,10) (27,10) (19,14) (27,18) (14,25) (16,21) (33,28) (21,17) (12,24) (29,11) (4,29) (9,28) (8,29) (14,32) (18,1) (14,6) (14,23) (30,7) (16,7) (2,26) (18,3) (12,30) (32,5) (23,22) (33,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph220",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,16) (10,20) (21,17) (25,22) (21,18) (14,25) (13,0) (23,3) (2,26) (25,26) (26,5) (5,15) (18,12) (7,17) (27,1) (18,2) (11,25) (16,24) (17,9) (6,18) (24,19) (18,3) (15,16) (1,10) (13,8) (25,8) (20,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph528",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,21) (16,29) (10,30) (15,11) (28,6) (8,22) (26,7) (22,26) (0,11) (8,2) (13,11) (16,30) (19,1) (27,9) (12,20) (12,3) (30,27) (28,19) (29,25) (30,5) (12,24) (17,4) (24,17) (12,7) (14,13) (0,17) (30,23) (5,7) (1,12) (17,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph144",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,26) (8,12) (24,2) (17,20) (18,24) (16,26) (6,26) (21,20) (8,14) (0,11) (6,5) (3,11) (25,15) (19,10) (3,13) (9,17) (0,8) (1,4) (24,12) (15,16) (22,17) (22,3) (2,26) (10,23) (22,10) (4,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1680",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,9) (16,5) (10,25) (12,5) (12,24) (15,1) (28,6) (9,15) (4,20) (27,28) (31,9) (17,3) (22,1) (23,8) (1,0) (13,12) (26,24) (29,20) (2,22) (1,6) (23,19) (8,22) (1,18) (14,16) (29,21) (0,7) (27,20) (3,12) (9,12) (9,30) (16,0) (2,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1252",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,7) (0,7) (24,4) (20,12) (2,13) (0,19) (3,10) (1,16) (4,23) (16,26) (9,10) (26,4) (9,13) (6,18) (16,18) (21,2) (22,18) (11,5) (19,11) (27,24) (24,0) (25,3) (12,11) (1,0) (15,26) (11,8) (3,8) (0,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph671",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,5) (3,28) (4,22) (26,15) (22,7) (21,19) (10,23) (29,10) (4,29) (26,4) (13,18) (14,9) (0,31) (19,13) (9,29) (5,1) (16,2) (17,21) (12,9) (14,27) (8,6) (26,30) (20,3) (25,5) (8,21) (11,4) (20,5) (16,21) (0,8) (17,25) (0,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1991",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (3,0) (9,17) (5,15) (34,32) (20,21) (10,25) (24,3) (33,23) (31,19) (13,20) (9,18) (12,14) (2,0) (19,28) (31,26) (10,12) (28,27) (4,21) (23,2) (20,10) (7,1) (29,31) (6,11) (2,13) (24,7) (16,10) (8,13) (4,34) (0,18) (29,22) (0,28) (0,1) (10,11) (1,33) (5,16) (5,30) (4,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph911",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,31) (1,18) (28,30) (29,11) (16,7) (19,14) (26,0) (20,4) (4,29) (34,30) (33,10) (21,17) (27,10) (3,18) (24,12) (33,13) (32,23) (27,18) (2,26) (14,25) (8,29) (14,23) (2,16) (25,28) (22,8) (15,28) (30,12) (16,21) (32,5) (28,9) (8,7) (33,14) (14,6) (23,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1350",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,12) (23,4) (11,26) (15,13) (16,9) (10,14) (20,24) (0,3) (0,4) (7,18) (17,20) (2,0) (27,22) (6,26) (8,23) (16,19) (3,25) (27,24) (1,14) (18,19) (8,15) (17,14) (7,13) (22,2) (21,10) (21,23) (0,23) (24,25) (5,11) (17,5) (28,3) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph416",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,15) (16,11) (14,6) (11,23) (29,1) (1,24) (4,27) (7,28) (29,25) (2,19) (22,17) (21,0) (13,15) (10,16) (20,14) (8,28) (6,9) (28,23) (29,22) (23,1) (19,23) (16,18) (27,3) (0,27) (4,8) (26,5) (12,22) (23,14) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1152",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (4,0) (16,25) (7,23) (0,1) (0,15) (12,11) (2,10) (19,1) (22,5) (5,4) (25,11) (26,19) (0,2) (20,3) (8,11) (21,19) (18,6) (17,3) (12,3) (26,20) (21,24) (1,18) (12,14) (5,18) (3,0) (4,13) (2,11) (3,15) (9,3) (23,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1752",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (3,0) (16,15) (16,6) (30,20) (22,10) (29,11) (27,5) (31,29) (30,19) (26,10) (4,0) (24,7) (31,6) (20,13) (14,18) (0,1) (0,13) (25,29) (28,12) (15,9) (0,2) (8,23) (1,27) (4,2) (8,18) (32,19) (17,11) (4,23) (26,32) (29,13) (4,21) (8,24) (19,3) (28,7) (1,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph194",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,5) (16,20) (26,25) (16,22) (3,18) (15,22) (6,2) (17,24) (11,19) (6,4) (9,7) (1,14) (23,13) (26,10) (0,19) (0,12) (9,4) (17,0) (24,25) (7,15) (15,11) (1,23) (21,10) (16,1) (8,22) (10,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1411",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,7) (28,12) (17,2) (16,15) (20,9) (26,28) (17,20) (2,19) (11,10) (21,17) (8,5) (15,0) (24,15) (7,13) (1,0) (11,3) (18,10) (26,3) (29,25) (3,0) (2,0) (4,27) (11,4) (27,1) (24,21) (7,6) (10,22) (14,22) (29,2) (2,6) (7,10) (11,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1133",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,8) (13,23) (11,17) (7,0) (25,5) (0,1) (2,1) (19,12) (18,4) (9,6) (10,21) (3,24) (19,14) (13,10) (14,5) (8,4) (2,18) (15,22) (0,19) (0,3) (21,22) (20,4) (24,6) (7,4) (26,18) (22,9) (11,2) (2,0) (10,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1689",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,11) (15,10) (21,23) (4,8) (18,13) (2,21) (21,0) (12,17) (8,16) (5,17) (14,13) (3,7) (28,27) (6,24) (29,20) (1,29) (18,6) (23,9) (0,1) (22,5) (30,10) (25,10) (8,7) (14,26) (29,28) (15,3) (26,5) (0,11) (24,2) (17,31) (4,24) (10,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1014",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,0) (22,0) (25,13) (14,1) (7,2) (8,12) (20,23) (23,13) (18,15) (17,18) (4,16) (24,9) (0,2) (8,15) (19,24) (4,21) (11,10) (18,5) (3,25) (8,0) (11,21) (23,6) (15,25) (24,10) (24,6) (2,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph74",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,21) (18,21) (22,10) (7,10) (8,5) (11,16) (0,20) (9,11) (23,22) (13,22) (24,22) (12,4) (5,11) (25,0) (23,6) (4,19) (9,23) (17,22) (25,2) (3,19) (2,1) (19,15) (14,17) (7,12) (4,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph285",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,9) (17,16) (3,21) (2,19) (19,25) (21,14) (13,23) (2,5) (10,26) (20,1) (23,12) (25,16) (21,6) (13,14) (19,26) (24,3) (25,9) (20,11) (18,1) (23,8) (22,16) (19,4) (11,14) (27,14) (7,26) (20,15) (0,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1270",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,7) (9,0) (22,13) (25,2) (16,3) (7,8) (10,26) (18,27) (5,14) (3,23) (0,2) (24,20) (0,1) (1,8) (23,21) (17,5) (15,22) (6,4) (10,19) (13,23) (5,19) (21,17) (19,0) (12,14) (11,20) (25,11) (7,2) (18,1) (22,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph146",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,26) (12,10) (9,25) (11,0) (21,2) (22,5) (3,0) (7,6) (26,3) (20,11) (8,19) (22,23) (1,6) (25,18) (12,7) (20,17) (13,0) (11,2) (8,21) (16,0) (14,6) (15,18) (12,23) (4,8) (21,9) (0,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1834",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,15) (9,18) (6,31) (2,0) (9,11) (26,0) (21,8) (14,3) (10,5) (20,5) (21,32) (29,31) (17,23) (3,31) (18,17) (22,23) (33,16) (15,20) (30,33) (8,7) (12,27) (3,1) (1,0) (23,27) (2,21) (19,6) (21,28) (4,10) (13,16) (24,0) (0,6) (1,23) (30,4) (25,32) (21,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph387",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,0) (1,22) (12,6) (3,6) (14,21) (18,24) (11,7) (15,12) (4,16) (5,13) (16,25) (2,24) (17,10) (23,5) (20,13) (11,10) (22,0) (8,4) (1,19) (2,8) (27,28) (26,3) (28,21) (10,9) (10,26) (0,25) (8,11) (10,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1875",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,23) (5,18) (33,31) (21,8) (1,9) (2,0) (19,9) (17,16) (21,14) (5,32) (15,32) (20,28) (8,11) (1,0) (12,14) (20,1) (29,23) (10,19) (27,4) (4,18) (31,22) (15,22) (2,4) (26,1) (17,22) (4,0) (26,16) (24,29) (25,0) (14,23) (28,0) (30,14) (6,22) (13,24) (3,11) (31,23) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph596",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,18) (2,20) (17,5) (4,14) (29,12) (1,18) (2,26) (1,28) (23,16) (25,6) (11,25) (15,21) (16,7) (19,16) (30,17) (10,17) (0,19) (24,0) (25,4) (27,8) (29,20) (9,23) (27,13) (24,3) (6,20) (15,0) (25,8) (19,6) (4,22) (30,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph191",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,24) (4,9) (4,19) (21,10) (1,11) (5,3) (23,22) (24,1) (17,3) (17,7) (17,23) (1,21) (7,4) (0,2) (0,15) (16,22) (8,12) (14,26) (7,15) (12,4) (25,21) (14,23) (1,4) (20,4) (24,18) (13,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph105",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,11) (7,13) (20,17) (26,6) (10,14) (25,24) (25,26) (16,9) (20,24) (19,3) (15,8) (1,14) (13,15) (22,2) (18,7) (11,5) (17,5) (17,14) (23,0) (23,8) (4,23) (10,21) (19,21) (12,3) (23,24) (16,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph862",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,22) (24,12) (21,14) (1,31) (27,31) (4,25) (21,17) (27,17) (26,21) (3,23) (12,6) (12,28) (5,16) (14,0) (32,0) (4,5) (23,22) (15,14) (30,8) (33,28) (6,27) (9,18) (9,22) (30,5) (20,13) (15,7) (17,2) (6,19) (14,20) (21,4) (5,11) (27,29) (21,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1300",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,15) (28,8) (4,9) (1,13) (18,28) (13,10) (26,6) (4,24) (18,11) (5,24) (4,16) (12,20) (2,12) (3,24) (9,27) (15,17) (28,7) (23,15) (16,14) (12,25) (8,1) (1,0) (27,0) (16,6) (19,25) (3,19) (22,9) (8,25) (0,2) (26,21) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph760",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,7) (2,15) (19,32) (27,23) (1,4) (26,12) (11,12) (7,3) (19,28) (0,8) (8,11) (3,24) (11,22) (25,19) (20,18) (13,22) (15,5) (1,16) (9,32) (14,5) (31,9) (6,28) (26,29) (25,11) (27,1) (20,21) (17,3) (10,7) (16,21) (11,16) (17,14) (20,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph942",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (33,0) (15,1) (8,19) (8,34) (25,1) (8,18) (6,27) (34,2) (7,17) (20,5) (31,7) (15,23) (17,6) (14,3) (12,13) (9,18) (19,31) (4,32) (3,25) (4,26) (27,33) (25,4) (11,1) (22,34) (13,16) (17,15) (21,0) (29,5) (16,24) (10,28) (22,30) (24,1) (25,29) (10,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph95",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (18,21) (1,16) (9,13) (4,23) (15,7) (2,20) (11,19) (18,16) (3,10) (25,24) (8,11) (3,22) (12,11) (24,4) (17,12) (11,5) (0,14) (18,6) (3,8) (0,19) (9,10) (16,4) (7,0) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph311",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,17) (7,4) (14,9) (13,28) (10,26) (7,26) (3,20) (15,16) (24,28) (16,19) (21,20) (14,15) (5,1) (8,11) (2,28) (16,27) (28,18) (18,0) (9,21) (25,19) (20,5) (5,23) (16,17) (6,26) (8,15) (21,10) (12,20) (20,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph462",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,23) (22,28) (5,9) (17,7) (26,29) (20,15) (21,4) (11,2) (8,14) (13,15) (3,23) (12,19) (6,3) (9,27) (1,4) (24,0) (26,15) (6,0) (14,5) (23,15) (2,4) (19,26) (5,13) (19,11) (11,22) (10,11) (22,18) (16,7) (25,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1646",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,27) (17,24) (25,29) (16,3) (29,1) (13,25) (0,3) (23,22) (21,28) (13,19) (13,3) (27,15) (29,5) (21,14) (1,0) (7,5) (0,9) (2,29) (9,12) (26,13) (19,14) (31,10) (10,24) (22,8) (4,11) (0,2) (11,30) (7,20) (25,6) (29,17) (26,23) (11,9) (12,22) (18,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1841",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,0) (3,0) (2,32) (21,31) (20,6) (22,31) (9,12) (14,30) (3,19) (32,31) (30,8) (9,19) (20,5) (25,17) (33,4) (12,8) (11,29) (4,3) (15,22) (31,10) (1,29) (27,24) (24,29) (12,28) (17,26) (1,26) (18,6) (16,17) (1,19) (29,10) (0,1) (27,7) (0,4) (28,0) (22,23) (5,16) (13,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph907",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,16) (31,25) (28,1) (7,10) (13,25) (26,12) (12,33) (29,25) (1,5) (34,15) (8,18) (4,11) (34,14) (4,0) (19,1) (25,7) (17,12) (23,26) (1,29) (16,2) (30,3) (11,6) (5,9) (6,2) (12,5) (34,27) (20,13) (8,27) (28,24) (21,17) (18,13) (32,0) (30,5) (22,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph75",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,22) (0,3) (16,14) (13,20) (17,6) (0,8) (21,0) (23,15) (12,19) (13,21) (2,13) (16,12) (17,25) (17,23) (12,18) (24,15) (25,8) (5,2) (8,10) (19,1) (11,10) (1,25) (11,4) (7,14) (18,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1685",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,16) (2,4) (0,3) (31,6) (1,23) (28,12) (23,8) (1,26) (29,13) (0,2) (0,1) (4,23) (24,7) (20,13) (11,17) (19,3) (15,9) (28,29) (8,24) (27,5) (19,30) (27,7) (18,8) (6,16) (18,14) (30,20) (11,29) (25,29) (31,19) (13,0) (10,26) (21,4) (10,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph542",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,16) (30,15) (26,14) (6,20) (1,12) (28,5) (4,1) (27,23) (4,23) (1,20) (24,11) (25,24) (28,8) (2,14) (9,21) (6,21) (9,7) (19,30) (16,10) (11,8) (20,17) (28,23) (0,16) (19,6) (13,7) (22,4) (14,29) (26,0) (18,21) (3,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1647",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,24) (8,7) (23,9) (4,8) (10,27) (21,0) (4,24) (29,28) (18,13) (1,0) (15,10) (14,13) (0,11) (23,21) (17,12) (7,3) (2,0) (19,11) (31,17) (21,2) (27,28) (5,26) (29,1) (26,14) (16,8) (10,25) (18,6) (17,5) (29,20) (30,10) (5,22) (15,3) (24,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1065",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,19) (12,7) (12,22) (0,4) (12,3) (9,13) (10,11) (11,20) (0,3) (2,8) (25,4) (24,17) (19,1) (1,0) (17,6) (11,13) (0,5) (17,14) (16,18) (2,0) (23,7) (1,12) (21,17) (0,11) (16,5) (8,22) (18,0) (5,7) (12,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph887",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (9,30) (2,9) (16,33) (23,19) (25,21) (18,32) (3,2) (29,23) (22,16) (15,0) (33,27) (33,31) (0,6) (7,33) (8,30) (21,14) (13,29) (2,31) (2,29) (12,27) (20,9) (2,26) (12,15) (5,0) (20,10) (14,8) (18,1) (17,31) (25,24) (18,6) (28,32) (31,4) (12,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1581",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,14) (4,13) (24,14) (3,22) (20,10) (30,7) (2,0) (13,14) (0,18) (27,3) (11,20) (12,1) (21,10) (25,4) (28,8) (9,5) (23,21) (30,4) (15,16) (5,19) (10,6) (10,29) (2,6) (7,26) (19,28) (16,24) (17,22) (21,13) (12,0) (22,4) (0,1) (27,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph560",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (14,11) (19,6) (30,12) (19,27) (12,25) (13,25) (4,26) (10,16) (22,9) (28,7) (12,8) (3,4) (21,26) (8,24) (21,23) (16,2) (14,15) (1,3) (4,14) (20,29) (22,21) (7,12) (3,18) (20,2) (22,6) (5,9) (24,10) (17,10) (13,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1225",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,1) (17,25) (25,27) (22,27) (20,7) (7,1) (1,12) (23,2) (25,13) (27,21) (18,15) (9,3) (4,11) (2,21) (25,20) (13,0) (24,5) (15,14) (9,18) (9,6) (4,5) (26,0) (12,4) (1,0) (8,7) (10,14) (19,25) (16,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1812",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (4,16) (21,27) (1,10) (31,25) (5,6) (14,26) (5,27) (7,6) (23,13) (26,1) (30,31) (2,15) (20,8) (24,12) (33,5) (15,13) (20,21) (0,2) (30,18) (21,28) (2,12) (10,11) (0,3) (4,0) (33,29) (0,1) (16,3) (20,9) (32,13) (5,25) (26,22) (26,20) (0,9) (6,4) (12,6) (19,28) (17,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph137",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,23) (20,7) (5,12) (5,4) (0,9) (9,23) (20,14) (17,2) (15,7) (3,9) (22,5) (17,6) (16,21) (25,11) (13,0) (1,8) (8,21) (21,25) (2,24) (4,26) (13,4) (23,6) (7,19) (18,4) (21,10) (21,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1908",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,2) (0,1) (33,5) (22,23) (9,11) (7,24) (2,0) (13,21) (28,18) (32,4) (31,21) (29,18) (23,25) (10,19) (5,12) (18,34) (27,10) (9,16) (5,18) (22,1) (26,14) (0,31) (10,3) (13,25) (4,3) (6,5) (15,22) (4,30) (0,3) (7,4) (14,30) (13,30) (10,6) (2,20) (11,25) (8,7) (7,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph526",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,0) (12,16) (9,13) (9,18) (29,7) (17,9) (18,26) (2,3) (28,20) (2,22) (30,10) (15,30) (15,22) (0,28) (23,6) (11,4) (21,26) (25,0) (19,7) (2,24) (8,6) (28,14) (12,13) (8,14) (24,5) (3,0) (29,1) (23,4) (16,11) (14,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1774",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (2,0) (12,29) (20,23) (19,27) (30,32) (23,13) (6,14) (31,28) (31,17) (32,4) (3,6) (17,11) (32,10) (32,1) (31,16) (10,6) (27,21) (5,9) (24,4) (11,24) (15,29) (11,23) (27,9) (7,24) (1,0) (8,29) (25,3) (9,6) (2,18) (26,7) (22,25) (8,24) (1,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1506",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,28) (27,19) (25,23) (15,10) (0,24) (13,9) (28,20) (26,18) (3,20) (16,29) (12,22) (6,19) (0,2) (0,27) (5,26) (9,15) (20,13) (8,0) (3,12) (17,10) (29,12) (12,11) (3,0) (14,7) (5,16) (11,19) (28,21) (0,1) (11,1) (0,4) (2,1) (18,4) (7,16) (30,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph776",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,30) (16,14) (8,30) (7,22) (27,4) (14,13) (21,4) (7,26) (20,0) (29,14) (11,29) (2,6) (7,19) (14,31) (28,14) (27,18) (12,22) (15,24) (30,23) (9,24) (22,10) (26,8) (1,12) (14,6) (14,32) (32,9) (17,29) (25,28) (24,0) (20,3) (10,0) (12,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph864",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (22,32) (1,24) (23,4) (2,13) (1,27) (27,11) (29,26) (7,17) (17,4) (8,16) (7,6) (10,16) (1,12) (2,26) (17,30) (25,0) (23,15) (27,0) (17,21) (27,23) (27,33) (31,14) (27,20) (19,18) (28,22) (31,29) (5,8) (11,3) (10,29) (13,22) (9,19) (19,30) (5,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph570",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,21) (24,25) (25,30) (4,18) (9,16) (6,26) (3,11) (24,29) (0,24) (5,26) (25,2) (1,13) (9,23) (23,15) (17,2) (12,6) (26,18) (10,13) (15,14) (17,21) (11,0) (11,8) (22,24) (27,22) (7,1) (20,1) (1,12) (28,11) (15,29) (20,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1664",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,23) (26,1) (27,15) (8,4) (18,4) (20,16) (19,5) (28,30) (10,14) (24,25) (9,24) (21,19) (6,12) (7,26) (4,13) (11,15) (17,23) (29,6) (3,8) (14,6) (11,28) (3,0) (16,13) (1,0) (22,13) (13,31) (21,1) (11,24) (24,8) (1,9) (0,2) (30,0) (12,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph831",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,27) (27,31) (8,16) (26,28) (31,14) (23,32) (16,2) (17,0) (4,21) (16,22) (8,29) (18,3) (6,11) (5,16) (4,13) (14,30) (15,14) (11,8) (18,13) (9,17) (14,10) (27,1) (23,27) (7,22) (27,28) (12,9) (7,20) (1,18) (5,9) (25,0) (8,24) (22,33) (11,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph171",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,2) (15,16) (25,19) (26,20) (18,12) (6,13) (22,25) (25,17) (24,5) (1,17) (8,14) (11,16) (3,14) (14,10) (7,24) (4,9) (15,20) (22,20) (3,5) (6,5) (0,14) (2,4) (25,18) (19,23) (14,9) (16,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1352",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,11) (21,28) (11,10) (13,5) (1,0) (21,14) (27,28) (25,16) (3,26) (20,10) (2,8) (0,2) (3,0) (27,0) (18,24) (11,8) (12,6) (10,9) (0,25) (24,2) (0,22) (16,4) (3,6) (26,10) (1,22) (17,10) (13,20) (4,8) (1,19) (23,5) (15,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph515",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,29) (1,12) (10,29) (7,3) (26,21) (4,28) (9,19) (7,21) (24,27) (28,15) (18,0) (14,0) (13,18) (5,6) (22,16) (10,2) (23,4) (17,8) (0,26) (8,12) (17,9) (24,7) (12,27) (20,23) (11,12) (25,18) (30,23) (30,14) (5,28) (22,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph552",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,9) (23,17) (7,2) (17,14) (26,20) (1,22) (10,26) (14,16) (9,4) (28,17) (6,8) (5,16) (14,12) (24,29) (14,8) (11,7) (0,13) (13,28) (14,18) (15,20) (16,21) (28,2) (19,15) (9,3) (10,25) (19,22) (6,20) (29,7) (13,27) (1,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1339",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,5) (25,10) (26,16) (8,13) (27,8) (3,0) (14,11) (23,13) (27,20) (6,9) (21,17) (23,24) (13,2) (12,26) (22,18) (11,9) (19,17) (1,16) (8,21) (25,4) (2,0) (16,25) (0,1) (3,22) (15,22) (24,5) (7,12) (20,10) (0,7) (28,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph984",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,31) (24,29) (18,22) (9,15) (11,26) (20,21) (0,25) (5,12) (20,7) (5,4) (5,7) (12,6) (7,19) (20,3) (8,15) (34,12) (12,14) (10,12) (16,34) (17,1) (13,30) (9,32) (31,16) (28,32) (11,24) (18,30) (11,21) (32,30) (17,0) (4,33) (13,14) (27,12) (16,2) (23,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1181",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,6) (15,25) (19,2) (18,26) (12,1) (0,12) (3,6) (0,2) (4,7) (17,22) (7,11) (19,23) (20,8) (21,22) (19,18) (16,12) (12,24) (0,1) (23,8) (4,24) (0,3) (13,23) (9,19) (7,5) (10,5) (15,6) (21,16) (14,2) (17,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1468",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (20,16) (0,1) (24,27) (26,1) (4,5) (22,17) (2,16) (7,26) (0,4) (29,12) (0,3) (23,22) (0,2) (17,13) (25,12) (29,19) (23,14) (3,17) (27,14) (5,7) (17,26) (12,11) (16,17) (11,21) (8,28) (10,20) (21,18) (0,7) (7,9) (18,10) (12,8) (8,15) (26,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1806",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,27) (6,5) (16,8) (10,0) (17,28) (33,24) (6,21) (23,13) (0,31) (10,27) (1,4) (0,2) (18,5) (13,9) (1,0) (17,9) (14,15) (11,15) (2,1) (25,14) (12,1) (26,14) (2,20) (13,21) (6,8) (30,1) (12,26) (19,27) (22,5) (32,17) (3,7) (7,17) (0,3) (32,29) (24,5) (14,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph152",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,26) (26,9) (25,10) (4,23) (4,21) (16,22) (13,15) (22,9) (3,15) (11,7) (12,14) (15,2) (23,19) (0,9) (11,1) (8,17) (14,0) (20,18) (21,13) (7,0) (6,13) (8,7) (5,9) (9,19) (20,7) (21,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph774",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,1) (2,1) (20,2) (14,24) (26,14) (9,13) (10,0) (12,26) (11,15) (17,9) (13,21) (31,17) (22,5) (5,6) (28,17) (3,7) (5,32) (19,27) (7,17) (6,21) (1,29) (6,8) (8,16) (15,14) (5,18) (27,10) (25,32) (27,21) (1,4) (28,14) (13,23) (0,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph559",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,4) (1,23) (12,5) (4,8) (11,27) (2,24) (11,7) (23,30) (10,17) (14,30) (16,18) (10,2) (6,19) (0,10) (29,17) (14,28) (5,22) (19,22) (22,30) (13,21) (9,8) (1,26) (15,0) (14,3) (27,12) (29,23) (21,19) (14,16) (20,28) (25,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1484",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,28) (19,11) (15,3) (3,29) (9,1) (2,27) (10,2) (3,0) (18,3) (0,10) (2,7) (17,13) (13,1) (23,2) (6,1) (16,6) (1,26) (20,1) (12,4) (26,12) (0,1) (13,25) (13,24) (16,22) (8,20) (17,14) (2,0) (4,5) (29,21) (26,18) (17,2) (18,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1668",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,20) (23,1) (31,6) (23,8) (1,0) (28,29) (4,0) (8,24) (0,2) (10,26) (27,5) (0,13) (23,4) (13,29) (21,4) (6,16) (20,13) (7,24) (2,4) (18,14) (22,10) (27,7) (28,12) (15,16) (11,17) (9,15) (31,19) (0,3) (3,19) (25,29) (19,30) (1,26) (8,18) (29,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph912",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,26) (12,17) (21,5) (34,22) (31,4) (28,16) (12,34) (20,13) (25,12) (19,26) (5,3) (31,15) (23,5) (21,27) (0,9) (30,5) (2,6) (17,1) (23,11) (16,29) (23,26) (6,18) (8,2) (20,34) (27,31) (30,9) (28,6) (32,12) (2,12) (0,10) (16,7) (1,14) (24,6) (33,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1451",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (22,13) (27,22) (0,1) (23,13) (21,19) (0,23) (10,13) (1,14) (21,26) (29,25) (6,25) (12,17) (7,28) (3,6) (15,24) (13,20) (18,24) (8,21) (15,1) (27,6) (6,9) (4,24) (7,23) (29,2) (5,16) (19,11) (5,20) (16,19) (23,1) (4,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1914",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,21) (3,0) (6,17) (2,0) (23,0) (12,3) (22,12) (4,0) (16,33) (26,17) (7,23) (19,1) (34,18) (19,5) (13,22) (24,5) (0,17) (20,28) (14,34) (12,30) (32,31) (1,0) (18,30) (11,5) (17,1) (26,27) (20,15) (6,9) (20,27) (13,28) (12,4) (34,8) (4,32) (10,21) (29,31) (24,25) (11,16) (9,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph301",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (15,18) (15,11) (19,21) (2,5) (24,13) (17,0) (13,23) (5,8) (9,20) (14,11) (25,28) (25,11) (0,23) (17,1) (4,3) (6,9) (16,21) (19,26) (13,9) (7,13) (8,17) (26,3) (11,13) (0,26) (10,27) (14,27) (8,22) (12,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1790",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,12) (26,12) (20,30) (0,27) (11,21) (14,8) (26,13) (28,23) (23,24) (14,7) (1,25) (5,8) (4,12) (3,24) (29,9) (2,25) (9,13) (15,10) (19,31) (0,1) (5,30) (29,11) (13,24) (32,27) (16,24) (20,25) (17,2) (2,0) (6,11) (18,5) (5,21) (16,15) (5,31) (17,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1061",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,5) (1,0) (9,0) (23,3) (21,23) (24,2) (16,3) (8,7) (11,25) (22,13) (14,5) (7,4) (23,13) (19,0) (2,7) (8,1) (20,11) (10,1) (12,14) (21,17) (22,25) (15,22) (19,5) (19,10) (6,4) (20,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph508",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,2) (6,15) (29,14) (24,0) (0,30) (25,4) (28,14) (5,21) (23,20) (18,10) (23,27) (3,0) (6,12) (9,23) (5,13) (22,9) (1,22) (29,25) (4,19) (2,22) (24,18) (8,26) (7,12) (5,11) (24,26) (16,21) (3,20) (5,6) (14,27) (22,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph516",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,14) (6,15) (25,29) (22,9) (21,5) (21,16) (26,8) (18,10) (6,5) (24,18) (27,23) (24,0) (6,12) (12,7) (22,1) (20,23) (17,2) (28,14) (0,3) (11,5) (29,14) (2,22) (20,3) (5,13) (26,24) (22,21) (4,19) (25,4) (9,23) (0,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1593",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,29) (14,6) (4,20) (2,4) (22,29) (24,26) (15,1) (2,27) (16,8) (23,30) (22,8) (18,25) (25,21) (6,23) (3,5) (19,7) (14,13) (1,0) (17,10) (24,25) (11,29) (20,3) (0,4) (12,21) (22,26) (24,20) (15,0) (12,9) (3,0) (20,19) (0,2) (6,28) (27,13) (6,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1645",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,1) (31,18) (7,23) (17,6) (27,20) (9,2) (4,25) (26,27) (7,14) (0,2) (5,19) (20,28) (1,0) (18,30) (5,23) (15,0) (12,22) (20,10) (29,16) (4,12) (24,21) (30,12) (3,12) (24,31) (26,17) (11,16) (22,13) (13,28) (1,17) (8,6) (3,0) (4,0) (0,17) (11,5) (21,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph245",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (9,6) (2,15) (22,20) (19,1) (20,9) (2,18) (9,4) (6,17) (21,27) (0,14) (9,26) (3,14) (24,23) (15,8) (2,26) (2,14) (10,21) (11,2) (12,13) (21,16) (7,21) (8,5) (19,23) (25,27) (26,27) (7,1) (12,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph722",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,10) (28,21) (0,26) (1,14) (8,25) (12,18) (23,21) (31,18) (0,32) (31,2) (21,18) (32,20) (18,25) (20,7) (9,27) (22,29) (4,25) (1,30) (8,9) (19,4) (21,10) (29,5) (11,5) (20,28) (22,17) (16,22) (11,21) (11,3) (13,6) (20,13) (27,1) (31,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph188",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (17,15) (7,15) (25,8) (23,25) (10,0) (21,25) (19,1) (9,13) (5,8) (20,1) (14,10) (4,8) (15,0) (23,26) (3,22) (9,23) (16,2) (2,12) (6,13) (4,2) (24,20) (9,3) (2,19) (11,8) (9,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1293",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (19,18) (4,3) (17,11) (12,15) (13,0) (6,16) (16,7) (15,10) (16,12) (23,8) (0,26) (14,3) (5,14) (15,2) (27,24) (11,13) (2,0) (6,14) (1,0) (1,8) (24,25) (2,18) (17,27) (9,18) (3,0) (16,22) (8,13) (5,20) (9,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph712",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,28) (2,27) (23,18) (11,28) (0,29) (20,9) (5,26) (32,7) (21,4) (32,14) (18,22) (23,4) (14,4) (13,2) (13,32) (23,10) (16,24) (28,26) (27,17) (27,24) (9,3) (6,29) (12,6) (8,2) (31,23) (25,23) (5,3) (1,5) (32,0) (0,30) (18,15) (26,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph386",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,13) (26,0) (8,5) (11,14) (17,0) (25,28) (11,13) (20,9) (11,25) (4,3) (1,17) (27,14) (2,5) (22,8) (23,13) (3,26) (16,21) (0,12) (10,27) (13,9) (21,19) (24,13) (15,18) (11,15) (19,26) (6,9) (0,23) (17,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1937",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (32,10) (29,19) (28,0) (19,15) (0,1) (29,5) (28,26) (33,23) (0,30) (0,3) (11,7) (0,33) (2,13) (15,25) (6,7) (12,17) (25,33) (1,4) (31,25) (28,14) (8,26) (2,10) (2,18) (0,2) (24,18) (7,3) (14,34) (17,13) (22,11) (17,21) (6,31) (20,31) (16,27) (9,10) (27,11) (4,26) (9,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph810",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,8) (20,26) (17,32) (14,28) (21,13) (0,33) (3,8) (23,10) (26,6) (7,2) (32,11) (26,19) (1,27) (7,14) (8,28) (15,4) (8,10) (25,12) (8,16) (13,22) (9,25) (1,26) (12,0) (29,18) (11,30) (14,17) (11,5) (12,24) (13,9) (29,15) (4,6) (31,33) (20,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph400",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,13) (17,9) (0,18) (9,19) (10,29) (3,7) (4,28) (0,26) (27,24) (29,23) (2,10) (21,7) (17,8) (7,24) (5,6) (12,1) (24,22) (0,14) (28,15) (12,27) (28,5) (20,23) (4,23) (21,26) (22,16) (8,12) (11,12) (18,25) (4,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1431",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,28) (21,8) (22,3) (28,12) (0,5) (0,3) (0,13) (23,6) (15,10) (28,1) (20,27) (28,13) (27,23) (4,16) (14,28) (13,2) (24,11) (18,15) (9,25) (28,26) (8,17) (7,21) (5,27) (0,2) (10,4) (24,10) (1,0) (3,4) (18,29) (20,19) (2,3) (18,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph173",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (4,14) (4,7) (26,12) (19,11) (25,18) (21,9) (18,11) (19,15) (13,12) (22,10) (16,13) (15,22) (21,3) (22,5) (20,25) (14,19) (24,17) (1,2) (17,19) (1,9) (6,24) (13,24) (3,14) (23,0) (8,11) (16,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph122",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,3) (11,12) (22,13) (11,16) (19,4) (8,26) (10,9) (14,16) (1,25) (24,10) (8,19) (9,26) (21,8) (16,9) (18,17) (6,12) (1,2) (6,15) (16,5) (4,18) (0,21) (8,23) (24,3) (7,3) (13,10) (3,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph29",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,23) (15,19) (2,11) (1,6) (2,7) (16,22) (5,14) (12,20) (9,5) (15,17) (23,11) (18,21) (8,23) (3,4) (25,24) (12,16) (0,2) (13,23) (17,13) (21,12) (9,2) (17,24) (9,6) (10,12) (23,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1662",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,19) (9,12) (26,22) (8,12) (19,4) (26,19) (5,30) (0,3) (28,7) (21,31) (26,21) (0,26) (8,3) (9,30) (13,27) (1,15) (1,18) (8,24) (0,2) (7,4) (7,17) (18,10) (11,17) (16,20) (29,5) (20,25) (6,23) (4,0) (21,13) (11,14) (24,15) (16,23) (0,1) (26,9) (3,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1857",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,1) (10,29) (9,19) (29,1) (25,17) (0,1) (13,2) (31,10) (8,30) (33,4) (6,20) (29,24) (22,15) (29,11) (4,3) (24,27) (22,31) (14,30) (16,5) (17,16) (26,1) (19,3) (31,32) (17,26) (12,9) (20,5) (0,2) (22,23) (2,32) (6,18) (27,7) (28,0) (28,12) (8,12) (21,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1474",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,19) (28,12) (9,11) (0,22) (25,22) (1,0) (0,20) (20,4) (2,1) (11,17) (17,15) (24,22) (26,22) (21,23) (5,11) (19,4) (23,9) (14,29) (10,7) (21,19) (23,6) (0,3) (12,4) (14,7) (8,5) (22,13) (10,27) (25,2) (16,19) (0,2) (7,25) (18,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1780",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,2) (5,11) (7,23) (0,11) (20,26) (29,21) (21,16) (1,0) (27,20) (1,25) (28,15) (0,2) (3,9) (24,8) (15,9) (28,12) (25,11) (28,30) (3,21) (0,13) (17,29) (8,18) (27,8) (4,21) (10,19) (29,7) (22,14) (7,10) (0,32) (11,14) (12,14) (6,0) (26,31) (19,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph371",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,19) (7,9) (28,8) (13,7) (5,28) (4,23) (20,1) (23,24) (21,17) (22,11) (12,1) (16,28) (15,20) (14,25) (21,24) (2,14) (6,28) (14,26) (0,26) (1,4) (18,6) (27,23) (20,6) (16,10) (11,8) (18,3) (9,21) (0,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph275",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,9) (26,24) (7,18) (7,13) (19,3) (20,24) (22,2) (23,0) (24,25) (14,17) (5,11) (17,5) (27,25) (22,21) (23,4) (17,20) (23,11) (14,10) (23,8) (10,21) (12,3) (15,8) (18,16) (6,26) (13,15) (19,27) (1,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1476",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,9) (6,29) (0,1) (8,23) (13,28) (0,26) (17,12) (26,2) (7,3) (28,22) (29,26) (6,21) (25,20) (20,12) (8,16) (22,15) (4,23) (21,10) (17,0) (18,13) (1,19) (23,11) (21,24) (20,1) (28,4) (24,27) (2,0) (5,6) (15,12) (9,3) (14,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph586",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,28) (19,4) (18,6) (29,18) (20,23) (16,6) (0,14) (10,4) (7,3) (17,1) (14,25) (4,7) (15,24) (14,12) (25,7) (12,2) (11,5) (2,15) (28,26) (27,15) (22,13) (9,12) (15,30) (11,6) (2,1) (26,12) (12,22) (16,21) (8,30) (20,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1623",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (25,5) (3,5) (12,18) (2,0) (23,5) (17,1) (22,12) (9,30) (24,16) (15,31) (20,6) (16,26) (1,14) (21,27) (18,6) (2,6) (16,7) (3,0) (31,4) (16,28) (11,23) (20,13) (0,4) (0,1) (23,26) (29,27) (0,9) (26,19) (12,17) (2,8) (30,12) (31,2) (6,28) (21,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph431",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,7) (7,17) (16,9) (2,6) (7,29) (0,6) (3,26) (28,12) (28,1) (27,4) (11,24) (11,22) (25,7) (8,12) (8,11) (21,4) (10,14) (20,21) (1,15) (8,27) (25,19) (13,23) (22,14) (22,23) (0,18) (16,5) (10,3) (0,1) (5,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1599",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,6) (13,23) (29,3) (10,25) (14,30) (20,10) (7,12) (26,12) (25,4) (17,21) (25,16) (18,22) (13,8) (19,22) (30,27) (11,9) (2,0) (28,0) (7,0) (0,3) (3,24) (27,20) (11,15) (8,21) (5,24) (1,0) (16,29) (17,22) (5,9) (26,23) (16,1) (13,2) (8,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1437",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,28) (26,12) (23,15) (0,2) (22,20) (29,15) (0,14) (6,16) (10,6) (3,7) (11,22) (9,4) (14,24) (7,25) (2,12) (25,15) (1,13) (15,2) (11,5) (0,1) (3,0) (18,27) (18,6) (0,20) (14,12) (1,2) (12,21) (16,19) (0,4) (8,12) (17,4) (6,28) (4,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1088",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,16) (20,4) (4,2) (23,22) (5,14) (11,10) (7,17) (15,21) (4,1) (0,1) (19,15) (13,5) (18,22) (3,6) (0,6) (2,0) (2,11) (22,25) (8,14) (24,9) (4,0) (19,12) (15,13) (0,3) (23,7) (15,22) (0,11) (5,9) (23,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph472",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,19) (23,6) (17,11) (24,22) (12,4) (2,25) (7,25) (19,21) (7,14) (22,0) (17,15) (22,25) (1,2) (11,9) (18,22) (14,29) (26,22) (13,22) (12,28) (5,8) (23,21) (20,0) (11,5) (4,20) (19,16) (7,10) (3,19) (10,27) (9,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1836",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,28) (23,14) (17,33) (32,25) (32,21) (20,0) (29,27) (1,13) (8,3) (31,10) (16,10) (31,30) (12,27) (21,18) (17,15) (4,8) (7,32) (13,14) (9,26) (10,8) (18,3) (4,27) (2,8) (12,11) (31,22) (21,6) (1,4) (9,19) (20,6) (15,6) (32,24) (1,0) (9,30) (19,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph66",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,21) (8,12) (21,1) (21,24) (4,9) (24,16) (15,0) (3,13) (22,1) (17,7) (2,0) (23,20) (25,23) (6,24) (15,22) (19,4) (4,1) (17,3) (12,4) (18,4) (14,7) (7,4) (17,23) (11,1) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph602",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,10) (8,23) (15,31) (22,28) (20,17) (29,16) (12,17) (19,23) (29,8) (15,29) (0,13) (14,31) (31,9) (11,30) (24,22) (6,0) (23,21) (16,18) (15,4) (7,29) (26,24) (2,1) (26,2) (3,27) (13,10) (19,11) (30,5) (8,27) (2,25) (26,18) (20,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1573",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,28) (17,14) (2,19) (4,14) (28,12) (24,12) (26,29) (5,17) (14,7) (0,3) (28,6) (29,23) (19,14) (2,0) (15,16) (13,30) (15,25) (6,23) (9,8) (0,29) (10,18) (9,15) (6,1) (0,1) (11,28) (20,12) (2,30) (25,17) (22,10) (3,4) (1,15) (21,7) (18,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1172",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (23,8) (1,0) (5,11) (13,7) (11,22) (3,12) (13,15) (26,6) (24,25) (19,3) (2,22) (5,17) (25,26) (14,10) (1,14) (2,0) (9,16) (17,20) (8,15) (21,19) (23,4) (17,14) (20,24) (7,18) (24,23) (21,10) (16,18) (0,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph625",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,23) (5,3) (27,17) (10,23) (26,5) (31,20) (28,11) (26,13) (7,5) (3,9) (26,4) (21,9) (0,23) (28,19) (6,12) (23,18) (4,22) (0,30) (1,20) (16,24) (24,18) (15,18) (27,25) (14,4) (8,2) (28,2) (23,27) (2,13) (14,1) (0,29) (6,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph278",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,3) (26,19) (3,20) (13,2) (14,4) (11,12) (2,11) (6,15) (25,22) (7,18) (27,0) (1,19) (26,11) (5,4) (23,8) (12,3) (3,10) (19,21) (12,15) (17,24) (16,3) (1,18) (25,21) (9,11) (27,20) (5,18) (23,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph43",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,12) (18,22) (6,12) (5,11) (1,22) (8,5) (17,4) (21,5) (23,9) (0,22) (5,6) (19,9) (13,21) (25,20) (23,20) (16,24) (15,2) (23,14) (4,25) (10,6) (22,2) (18,7) (14,0) (14,24) (21,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph790",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,29) (17,28) (14,28) (20,9) (9,12) (23,16) (24,6) (26,8) (26,18) (5,22) (31,6) (4,3) (20,15) (4,25) (18,9) (26,27) (4,24) (19,13) (20,7) (21,26) (22,25) (29,10) (23,32) (2,0) (4,16) (10,2) (30,13) (6,13) (27,11) (6,1) (9,19) (28,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph727",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (9,1) (19,9) (14,16) (0,26) (22,29) (10,8) (18,7) (29,9) (2,15) (32,30) (18,14) (21,23) (17,32) (26,10) (14,1) (20,30) (31,3) (3,6) (11,9) (6,19) (15,18) (0,28) (12,9) (25,5) (4,19) (17,15) (21,2) (24,2) (13,16) (24,27) (19,8) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1821",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (25,16) (17,26) (2,0) (25,29) (17,24) (21,11) (27,9) (11,9) (17,5) (7,10) (0,5) (21,31) (32,16) (10,32) (19,33) (1,0) (15,12) (8,1) (11,28) (0,3) (3,32) (30,19) (23,22) (25,11) (12,6) (4,8) (23,30) (33,2) (14,1) (18,2) (24,23) (12,20) (8,0) (13,31) (6,7) (6,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph587",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,4) (18,12) (29,7) (11,14) (12,0) (21,9) (4,16) (0,17) (8,20) (25,14) (28,30) (8,15) (26,22) (5,11) (14,4) (15,24) (17,7) (11,13) (2,8) (23,11) (28,10) (20,25) (21,3) (0,21) (22,27) (10,5) (1,15) (27,19) (19,21) (16,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1950",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,12) (7,19) (27,32) (21,32) (1,5) (17,34) (3,33) (12,27) (16,28) (25,22) (30,32) (12,34) (24,14) (5,8) (22,13) (32,5) (29,0) (10,19) (26,2) (24,3) (16,2) (30,15) (9,6) (11,5) (2,14) (20,23) (9,11) (5,14) (29,14) (24,18) (19,24) (0,1) (27,20) (31,0) (25,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph850",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,2) (14,16) (13,19) (22,33) (12,5) (1,29) (16,2) (0,4) (6,11) (7,25) (17,12) (9,21) (10,7) (18,8) (25,13) (12,26) (5,30) (28,24) (27,22) (8,27) (15,1) (28,1) (14,12) (30,3) (26,23) (13,18) (20,17) (25,29) (1,5) (0,32) (25,31) (4,11) (5,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1888",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,9) (3,33) (20,21) (2,30) (25,17) (14,25) (24,26) (15,8) (30,10) (12,1) (23,21) (2,0) (27,7) (3,0) (22,19) (15,29) (16,2) (28,1) (0,5) (0,1) (1,7) (32,12) (10,28) (11,22) (18,33) (25,0) (29,16) (13,16) (6,10) (32,5) (0,30) (0,4) (23,28) (4,15) (31,11) (19,23) (17,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1034",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,10) (8,21) (16,25) (13,23) (22,18) (14,11) (5,9) (19,17) (11,9) (16,8) (0,1) (20,25) (2,13) (7,0) (24,5) (22,15) (21,17) (3,0) (9,6) (8,13) (1,16) (4,25) (12,23) (7,12) (22,3) (24,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph521",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,26) (27,0) (9,6) (14,30) (4,3) (26,3) (30,8) (22,19) (28,29) (5,2) (27,10) (17,0) (0,23) (13,11) (24,8) (17,25) (30,20) (12,0) (18,15) (21,9) (30,11) (26,13) (15,11) (13,7) (9,13) (14,29) (17,1) (8,5) (21,16) (13,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph645",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,17) (0,7) (1,21) (16,31) (2,19) (4,28) (20,11) (25,18) (19,7) (16,20) (29,8) (27,13) (5,15) (1,4) (0,24) (5,19) (26,4) (10,26) (2,11) (2,3) (12,31) (3,9) (8,17) (9,17) (16,14) (4,27) (23,30) (30,13) (7,18) (26,9) (21,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph442",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,21) (3,23) (8,1) (20,22) (4,9) (14,5) (23,29) (4,7) (7,8) (28,13) (21,17) (6,29) (13,29) (11,24) (29,5) (19,0) (26,2) (3,18) (22,16) (15,14) (10,19) (0,12) (7,2) (1,10) (25,28) (19,5) (17,27) (20,28) (11,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1315",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,12) (15,5) (21,19) (23,9) (8,1) (18,7) (16,20) (17,27) (7,20) (27,22) (21,4) (11,25) (17,2) (21,10) (4,28) (1,0) (14,28) (9,3) (20,23) (25,5) (13,0) (24,7) (4,13) (0,9) (6,27) (2,26) (4,5) (21,8) (23,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph219",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,18) (21,10) (14,23) (4,22) (1,11) (7,15) (17,23) (3,5) (1,4) (24,6) (12,8) (0,15) (23,24) (1,21) (4,20) (9,4) (17,7) (17,3) (3,13) (14,16) (16,27) (4,12) (21,26) (4,7) (25,1) (24,19) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph835",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,18) (15,28) (25,14) (4,29) (24,12) (14,23) (22,23) (6,14) (5,32) (8,29) (7,16) (4,20) (3,18) (28,33) (18,27) (2,16) (25,28) (8,22) (7,30) (9,28) (12,30) (11,29) (17,21) (33,10) (32,14) (14,19) (33,13) (26,0) (2,26) (16,21) (23,31) (10,27) (8,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph258",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,19) (26,4) (18,21) (14,27) (17,26) (8,6) (17,12) (1,22) (24,10) (3,10) (17,7) (6,7) (22,12) (24,21) (20,21) (13,24) (11,18) (11,15) (19,2) (7,16) (24,7) (9,14) (5,3) (27,25) (6,0) (27,23) (27,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1248",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,10) (25,1) (22,14) (7,5) (16,9) (7,23) (14,10) (12,26) (2,0) (18,21) (0,17) (3,24) (5,16) (8,25) (20,22) (11,22) (23,13) (7,11) (27,7) (0,6) (4,19) (11,8) (15,1) (6,2) (0,1) (11,21) (8,12) (4,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph204",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,17) (11,12) (0,27) (19,1) (13,2) (3,16) (14,4) (22,25) (12,3) (23,8) (11,2) (11,9) (4,5) (23,5) (19,21) (10,3) (3,20) (15,6) (26,11) (27,20) (5,18) (21,25) (26,19) (18,1) (12,15) (7,18) (17,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1222",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,11) (11,19) (26,18) (6,19) (27,23) (9,15) (24,23) (5,16) (4,18) (1,11) (13,9) (5,25) (7,14) (12,21) (2,1) (15,10) (8,0) (1,0) (27,0) (3,20) (22,0) (17,10) (12,3) (23,20) (12,26) (16,7) (13,20) (19,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1291",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,5) (3,15) (12,26) (8,20) (23,13) (1,26) (22,13) (27,18) (1,0) (1,19) (7,25) (18,26) (11,18) (20,16) (17,14) (16,6) (6,1) (24,2) (2,21) (10,2) (1,9) (17,2) (2,7) (10,0) (11,3) (1,13) (4,12) (13,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph794",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,1) (19,25) (17,14) (3,7) (22,11) (11,8) (4,1) (9,31) (7,30) (6,28) (21,20) (13,22) (20,18) (23,27) (19,28) (0,8) (11,25) (11,12) (17,3) (7,10) (16,1) (16,11) (5,14) (12,26) (5,15) (19,32) (9,32) (3,24) (16,21) (3,20) (29,26) (15,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1694",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,24) (21,11) (25,3) (12,23) (11,1) (9,16) (15,10) (5,20) (27,11) (28,22) (2,10) (29,27) (13,16) (12,14) (23,24) (21,30) (24,18) (24,22) (25,5) (2,0) (19,24) (15,31) (26,19) (28,6) (23,13) (29,7) (0,1) (8,29) (13,17) (31,13) (28,5) (29,4) (0,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1481",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,24) (2,0) (25,11) (25,28) (10,1) (29,13) (4,7) (13,28) (22,16) (7,2) (28,20) (14,5) (0,12) (0,19) (1,8) (29,23) (21,17) (20,22) (5,19) (26,2) (15,14) (1,0) (8,7) (23,21) (23,3) (5,29) (17,27) (4,9) (10,19) (3,18) (6,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph340",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,26) (11,25) (0,2) (16,25) (27,13) (23,17) (14,20) (25,27) (12,28) (4,21) (18,1) (12,6) (7,6) (14,10) (25,6) (15,6) (7,8) (12,5) (8,22) (19,23) (9,5) (3,21) (2,5) (26,15) (21,14) (24,11) (18,14) (26,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1982",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (15,18) (20,6) (1,16) (17,20) (4,32) (33,5) (2,18) (25,24) (4,6) (32,27) (34,2) (7,10) (14,13) (23,0) (3,26) (28,19) (4,22) (1,0) (9,7) (18,6) (11,24) (10,31) (7,14) (1,14) (22,29) (7,32) (10,26) (25,20) (18,21) (24,19) (30,21) (34,8) (11,12) (0,6) (17,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph664",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,1) (3,5) (13,20) (24,18) (23,28) (12,23) (6,27) (10,29) (30,13) (24,3) (22,17) (31,13) (18,19) (14,4) (24,20) (27,4) (9,0) (9,5) (9,26) (3,16) (1,7) (14,8) (25,21) (6,21) (10,19) (24,1) (0,22) (19,15) (16,23) (6,17) (2,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1253",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,3) (8,14) (1,0) (5,0) (25,5) (14,4) (15,9) (16,21) (18,15) (12,7) (3,1) (26,27) (19,5) (15,13) (17,20) (7,6) (10,16) (3,22) (8,6) (27,5) (21,2) (22,8) (24,21) (23,6) (9,14) (15,20) (11,10) (25,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph117",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,18) (3,19) (13,23) (22,5) (25,6) (9,25) (7,21) (14,13) (8,21) (10,20) (11,24) (4,3) (0,13) (5,0) (23,1) (17,20) (13,6) (4,10) (14,18) (2,24) (26,6) (21,18) (2,3) (16,8) (4,12) (10,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph289",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,7) (0,19) (4,15) (21,23) (7,8) (9,3) (13,1) (20,3) (6,17) (0,1) (22,17) (18,24) (6,27) (8,12) (5,20) (0,10) (2,23) (4,23) (6,2) (19,16) (16,7) (13,18) (25,2) (26,7) (17,0) (23,11) (3,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1302",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,25) (18,1) (14,10) (23,19) (15,6) (21,3) (20,14) (27,13) (16,25) (5,2) (12,28) (27,25) (6,7) (26,19) (12,5) (8,22) (24,11) (26,15) (7,8) (5,9) (14,21) (11,25) (2,0) (1,0) (21,4) (26,14) (12,6) (18,14) (23,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph856",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,21) (14,30) (4,9) (28,26) (26,27) (18,11) (10,3) (20,15) (17,32) (4,25) (26,8) (13,16) (30,12) (31,7) (28,2) (31,21) (19,33) (30,13) (27,24) (9,5) (0,23) (1,23) (1,9) (7,23) (14,2) (0,15) (26,6) (5,33) (10,18) (32,11) (27,32) (14,29) (0,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph244",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,25) (19,21) (22,13) (1,15) (13,9) (18,15) (1,23) (23,7) (23,0) (14,4) (26,6) (22,27) (13,23) (20,5) (1,12) (19,10) (21,24) (4,24) (5,16) (11,17) (6,2) (3,21) (6,8) (17,24) (27,6) (13,20) (16,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph546",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,28) (0,8) (13,17) (26,15) (25,10) (20,17) (29,3) (28,10) (4,1) (20,23) (28,6) (9,26) (15,16) (30,16) (2,26) (8,12) (12,24) (3,14) (24,2) (4,23) (22,27) (8,18) (5,6) (22,17) (28,11) (19,24) (7,26) (21,10) (11,0) (22,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1345",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,15) (26,16) (7,23) (5,25) (2,7) (1,0) (6,0) (11,23) (20,8) (6,14) (2,10) (27,13) (20,25) (2,0) (5,1) (4,28) (14,26) (10,15) (18,19) (26,22) (11,1) (0,18) (3,0) (8,24) (17,15) (3,18) (16,15) (1,9) (13,12) (27,4) (1,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1083",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,12) (0,6) (5,12) (19,9) (8,17) (6,24) (7,15) (16,20) (3,1) (4,19) (5,4) (19,6) (4,0) (3,4) (17,14) (10,22) (18,13) (6,21) (6,20) (4,7) (2,0) (1,0) (13,0) (14,24) (25,13) (22,4) (2,23) (0,3) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph512",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (16,13) (28,1) (21,11) (24,22) (29,21) (24,4) (3,19) (15,0) (4,7) (1,12) (15,4) (22,25) (23,27) (12,9) (6,13) (5,3) (10,4) (16,14) (20,7) (4,26) (6,30) (1,4) (17,3) (18,30) (23,17) (1,21) (8,24) (7,17) (14,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph267",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (25,6) (12,15) (18,2) (21,5) (10,25) (19,0) (15,26) (23,20) (26,13) (9,14) (13,20) (23,22) (9,2) (11,24) (20,16) (25,8) (8,17) (1,0) (10,3) (8,7) (7,5) (1,4) (27,12) (2,17) (18,13) (17,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1670",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,24) (4,23) (10,0) (20,3) (10,28) (20,26) (9,30) (21,19) (4,13) (17,15) (20,7) (8,20) (5,30) (11,18) (29,3) (12,4) (2,17) (30,18) (14,19) (23,7) (25,17) (1,14) (31,19) (16,26) (0,1) (13,18) (27,15) (22,3) (17,31) (7,28) (20,15) (11,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph966",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,7) (23,33) (13,24) (8,25) (16,22) (13,18) (31,14) (9,12) (22,34) (17,9) (28,27) (18,3) (15,14) (14,10) (14,32) (16,2) (22,7) (5,9) (23,27) (8,11) (8,16) (29,28) (5,16) (27,1) (17,0) (20,27) (8,30) (4,21) (0,26) (19,11) (11,6) (1,18) (4,34) (31,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1041",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,2) (0,2) (25,10) (4,20) (5,19) (2,4) (4,0) (0,13) (1,8) (1,0) (7,0) (16,23) (22,14) (9,19) (12,1) (21,12) (16,25) (7,24) (15,19) (3,17) (6,8) (11,9) (16,19) (18,6) (14,0) (20,12) (0,3) (17,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph736",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,9) (23,5) (9,22) (29,22) (13,12) (29,1) (0,31) (17,13) (18,11) (30,32) (27,14) (10,28) (3,16) (21,19) (5,3) (24,11) (20,30) (26,19) (20,11) (10,2) (2,1) (19,12) (15,2) (24,22) (5,6) (26,3) (24,8) (4,29) (28,14) (12,30) (8,7) (31,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph877",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (15,4) (33,31) (8,28) (20,8) (12,24) (17,32) (13,9) (20,26) (26,6) (14,28) (21,13) (8,12) (32,11) (13,22) (14,7) (9,25) (27,1) (19,26) (30,11) (5,11) (29,15) (23,10) (8,3) (12,0) (29,18) (14,17) (2,7) (8,10) (0,33) (16,8) (26,1) (12,25) (4,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1066",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,20) (0,3) (2,0) (5,3) (4,8) (22,7) (9,25) (16,0) (20,23) (8,11) (24,11) (0,1) (15,7) (1,20) (3,18) (7,12) (18,25) (17,12) (0,14) (17,3) (15,11) (16,21) (13,23) (14,24) (23,6) (5,1) (2,19) (10,22) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph532",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,2) (0,2) (20,17) (16,7) (12,17) (25,21) (1,21) (6,29) (27,7) (23,14) (5,13) (24,10) (17,16) (14,4) (24,23) (10,3) (20,1) (26,24) (18,30) (11,3) (23,1) (4,8) (25,15) (1,22) (28,19) (9,19) (18,9) (16,13) (27,28) (29,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph357",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,10) (8,17) (15,12) (26,24) (14,3) (12,16) (0,28) (25,19) (20,14) (11,23) (24,22) (17,13) (4,5) (9,7) (16,1) (26,10) (9,21) (21,14) (7,11) (21,4) (0,19) (18,5) (15,26) (26,2) (9,10) (27,23) (4,28) (17,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1469",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,24) (5,0) (21,2) (24,25) (15,13) (3,1) (8,6) (8,28) (6,26) (22,28) (10,3) (14,28) (23,8) (3,22) (4,14) (14,9) (12,7) (18,15) (15,9) (20,17) (6,7) (0,2) (15,20) (5,25) (16,10) (16,21) (0,1) (27,29) (5,19) (5,27) (11,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1639",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,28) (0,6) (13,2) (14,15) (1,0) (1,6) (16,9) (18,1) (22,21) (29,2) (4,5) (8,21) (25,14) (30,16) (0,3) (3,22) (20,27) (12,21) (22,26) (0,20) (0,24) (29,7) (25,11) (17,26) (19,16) (2,15) (4,27) (2,31) (23,30) (28,15) (15,12) (23,22) (2,0) (10,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph175",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (23,15) (21,9) (7,12) (18,1) (0,21) (5,4) (11,14) (25,15) (2,6) (22,8) (16,0) (15,16) (5,11) (5,18) (26,2) (24,0) (3,5) (7,14) (13,9) (3,0) (10,24) (19,5) (20,8) (26,10) (5,20) (17,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph381",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,26) (1,11) (4,12) (24,6) (14,16) (10,21) (23,25) (23,14) (24,20) (22,4) (17,7) (3,5) (7,4) (15,3) (27,21) (0,2) (15,0) (13,16) (19,22) (8,12) (3,17) (9,4) (28,13) (24,4) (1,21) (7,18) (1,4) (17,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1036",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,19) (5,4) (0,13) (14,16) (1,0) (14,3) (4,0) (5,22) (19,17) (0,2) (7,11) (22,19) (22,14) (3,0) (10,0) (25,23) (20,2) (8,4) (8,9) (21,1) (11,21) (10,2) (24,12) (17,10) (23,14) (12,5) (23,1) (18,19) (15,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1378",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,9) (12,9) (3,13) (16,15) (1,0) (6,0) (27,11) (21,23) (22,13) (26,7) (2,12) (23,26) (24,4) (5,26) (9,1) (6,26) (0,10) (1,8) (27,25) (28,6) (20,8) (15,1) (3,27) (18,24) (18,21) (18,3) (19,24) (20,14) (17,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1582",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,14) (25,10) (16,1) (0,2) (11,3) (12,8) (6,29) (14,26) (2,10) (2,28) (0,1) (18,13) (27,29) (1,17) (10,7) (23,24) (14,15) (9,12) (7,15) (30,21) (30,5) (9,22) (11,6) (21,0) (9,27) (17,25) (19,7) (20,9) (26,24) (13,26) (9,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1497",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,6) (4,9) (1,3) (23,8) (5,12) (26,4) (15,22) (0,13) (29,3) (17,7) (10,17) (2,7) (13,22) (19,4) (1,0) (21,20) (20,14) (26,5) (12,27) (5,16) (6,19) (2,3) (28,6) (24,6) (11,19) (24,14) (6,23) (4,25) (18,4) (13,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1826",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,18) (33,31) (0,12) (8,28) (8,20) (19,26) (8,3) (7,14) (2,0) (6,26) (7,2) (33,0) (21,13) (8,16) (0,3) (12,24) (12,8) (15,4) (13,22) (1,0) (10,23) (14,17) (1,27) (10,8) (28,14) (26,20) (30,11) (9,25) (9,13) (26,1) (4,6) (12,25) (11,32) (15,29) (32,17) (11,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1550",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,28) (0,2) (17,14) (11,7) (18,14) (28,2) (14,12) (8,14) (26,10) (29,24) (13,28) (13,27) (8,6) (7,2) (20,6) (0,1) (5,16) (4,9) (13,0) (14,16) (25,10) (22,1) (16,21) (3,9) (20,15) (19,22) (17,23) (19,15) (9,27) (0,3) (26,20) (29,7) (30,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph517",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (10,24) (12,6) (25,1) (18,4) (28,7) (3,26) (16,11) (16,9) (10,28) (0,30) (11,12) (6,20) (13,25) (3,24) (13,10) (21,18) (27,30) (15,3) (8,23) (9,0) (19,4) (16,14) (28,9) (1,5) (22,3) (26,8) (19,8) (8,29) (17,16) (2,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1901",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,34) (7,29) (17,6) (27,5) (4,15) (14,3) (0,3) (0,4) (8,18) (6,23) (1,0) (4,12) (30,14) (13,21) (9,34) (3,27) (0,2) (26,24) (9,26) (13,2) (14,2) (20,0) (16,34) (10,25) (33,7) (11,3) (31,3) (26,18) (9,1) (20,32) (3,19) (2,8) (32,25) (23,27) (25,3) (4,28) (22,5) (15,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1851",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,10) (3,18) (16,10) (21,18) (17,33) (22,31) (7,32) (27,29) (9,30) (31,30) (0,20) (1,4) (23,14) (32,21) (3,8) (32,24) (27,12) (2,0) (27,4) (32,25) (1,0) (9,19) (3,0) (11,12) (6,20) (2,8) (13,28) (8,4) (1,13) (8,10) (21,6) (13,14) (6,15) (15,17) (19,5) (9,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1097",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,24) (21,18) (6,8) (7,23) (1,15) (6,13) (14,24) (19,9) (22,25) (23,1) (19,21) (15,17) (13,23) (0,1) (3,0) (16,5) (4,12) (24,4) (19,16) (2,6) (23,0) (0,2) (10,17) (1,11) (3,21) (0,4) (5,20) (22,13) (13,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph599",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,21) (12,18) (4,13) (5,18) (11,10) (22,17) (12,30) (9,15) (2,3) (20,14) (24,7) (11,2) (19,1) (23,9) (19,23) (8,22) (5,21) (25,1) (0,20) (13,6) (18,24) (10,19) (11,27) (16,3) (8,28) (24,29) (22,10) (30,15) (13,23) (14,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1855",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,13) (11,15) (2,9) (12,7) (12,1) (2,11) (2,0) (31,0) (6,8) (16,28) (17,22) (25,18) (12,28) (25,14) (15,33) (19,18) (26,22) (2,31) (6,3) (21,16) (6,26) (12,10) (5,13) (28,4) (11,19) (0,27) (30,4) (32,18) (1,0) (3,23) (13,30) (8,19) (24,28) (23,24) (20,18) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1677",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,4) (12,10) (1,10) (19,30) (16,5) (3,24) (21,20) (13,2) (11,10) (27,19) (21,31) (0,18) (31,25) (24,7) (31,28) (12,14) (26,28) (23,2) (9,18) (2,0) (5,15) (9,17) (8,13) (1,7) (20,10) (20,13) (5,29) (1,0) (6,11) (29,22) (0,28) (10,16) (23,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph426",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,8) (5,2) (0,13) (3,17) (26,18) (16,24) (22,12) (19,29) (25,10) (0,2) (1,12) (23,14) (29,16) (15,19) (19,26) (26,27) (14,0) (25,7) (20,4) (6,21) (5,29) (2,4) (0,7) (9,11) (17,20) (28,26) (9,19) (12,20) (8,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1054",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (15,16) (3,14) (7,24) (17,25) (14,8) (15,20) (0,14) (17,1) (10,14) (3,0) (17,2) (1,0) (18,25) (5,23) (6,5) (16,21) (25,22) (11,16) (20,19) (24,22) (4,9) (2,4) (5,3) (19,25) (6,13) (2,0) (9,14) (18,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph305",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,21) (11,8) (26,15) (9,6) (22,26) (8,4) (16,8) (10,8) (11,26) (10,17) (14,2) (2,26) (20,0) (20,18) (13,9) (5,12) (23,20) (7,15) (7,5) (2,23) (1,15) (27,18) (6,2) (28,20) (7,25) (26,19) (22,3) (12,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph299",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,17) (24,0) (16,0) (7,14) (25,15) (2,26) (1,18) (12,9) (5,18) (20,8) (0,3) (21,8) (11,5) (11,13) (14,16) (6,2) (24,27) (5,4) (21,9) (27,26) (15,23) (5,20) (3,22) (19,0) (10,7) (16,15) (5,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1162",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (21,9) (19,11) (15,19) (22,10) (14,3) (4,7) (19,14) (21,3) (13,24) (22,15) (0,16) (20,25) (9,1) (11,8) (16,13) (18,11) (17,24) (2,0) (26,12) (22,5) (19,17) (18,25) (1,2) (4,14) (1,0) (12,13) (6,24) (0,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1817",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,33) (9,13) (12,26) (16,15) (32,5) (13,26) (33,0) (10,15) (20,25) (1,25) (22,31) (8,14) (33,18) (19,5) (30,20) (27,12) (12,4) (17,0) (13,24) (16,24) (2,25) (21,11) (1,0) (6,11) (29,9) (2,0) (17,2) (30,5) (29,11) (28,23) (14,7) (24,23) (5,21) (8,5) (24,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph815",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (16,19) (29,18) (19,13) (12,32) (23,30) (21,33) (1,11) (11,28) (30,17) (10,15) (7,27) (4,21) (15,12) (13,31) (21,0) (7,20) (8,31) (25,12) (15,5) (31,9) (23,32) (16,24) (12,6) (7,2) (18,22) (28,3) (14,11) (15,11) (20,33) (31,12) (16,26) (0,16) (10,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1309",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (15,22) (17,16) (3,27) (16,10) (8,28) (5,22) (13,15) (1,28) (23,18) (11,16) (5,27) (4,8) (6,14) (5,1) (19,14) (22,12) (0,3) (11,24) (0,27) (9,6) (0,4) (0,1) (23,1) (2,19) (1,21) (20,0) (25,4) (23,14) (23,11) (26,23) (2,0) (7,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph141",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (23,26) (17,12) (24,20) (4,20) (23,8) (12,19) (7,25) (3,10) (8,14) (23,11) (26,2) (20,1) (5,6) (16,13) (12,15) (1,13) (15,22) (18,4) (0,17) (6,22) (26,0) (6,21) (9,21) (24,21) (9,3) (7,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1816",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,29) (10,31) (13,22) (32,23) (19,7) (28,25) (1,8) (18,26) (19,21) (3,0) (17,0) (21,33) (30,9) (14,28) (24,0) (24,2) (6,16) (6,9) (3,12) (0,33) (27,5) (11,24) (17,16) (28,4) (14,15) (23,17) (1,0) (13,12) (31,28) (21,5) (20,24) (17,26) (8,30) (0,2) (31,3) (2,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1429",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,17) (20,6) (4,27) (18,23) (4,11) (12,15) (28,25) (8,0) (24,5) (14,22) (17,9) (19,0) (0,1) (9,24) (15,25) (29,0) (2,3) (10,29) (13,9) (7,14) (21,20) (19,21) (18,10) (2,29) (5,23) (12,27) (0,16) (22,26) (1,7) (26,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph375",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,0) (15,25) (16,5) (9,15) (25,4) (17,26) (7,25) (27,0) (28,24) (21,16) (25,24) (22,5) (23,16) (13,18) (20,12) (19,6) (8,22) (9,14) (16,7) (18,11) (25,6) (13,2) (0,11) (10,13) (4,2) (13,3) (5,1) (15,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph759",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,8) (1,28) (14,19) (16,12) (22,21) (18,0) (15,13) (24,19) (4,30) (26,6) (31,29) (18,5) (1,9) (7,14) (1,25) (17,0) (32,16) (19,20) (0,10) (29,18) (19,23) (2,23) (16,23) (14,15) (11,26) (30,3) (9,21) (27,16) (1,29) (26,14) (30,9) (14,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1653",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (9,21) (19,20) (7,14) (12,16) (19,23) (2,23) (30,29) (18,14) (0,1) (1,9) (31,23) (18,0) (26,11) (14,26) (25,1) (21,22) (30,4) (15,13) (1,16) (30,3) (28,9) (19,24) (28,8) (14,15) (18,29) (10,0) (6,26) (19,14) (1,29) (17,0) (18,5) (27,16) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph210",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,7) (18,21) (1,13) (22,6) (0,17) (22,20) (27,12) (3,0) (23,0) (12,18) (24,16) (3,10) (16,2) (9,15) (26,18) (17,4) (9,25) (12,20) (22,16) (9,22) (13,12) (5,24) (27,8) (3,7) (19,7) (11,5) (5,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1160",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,12) (1,24) (9,18) (15,22) (0,24) (20,0) (23,6) (25,7) (14,8) (18,21) (10,26) (19,14) (5,9) (11,16) (2,22) (3,2) (13,9) (6,8) (3,0) (26,15) (14,0) (4,11) (13,12) (4,23) (2,17) (19,7) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph23",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,10) (2,17) (2,7) (13,22) (16,19) (11,3) (16,6) (18,25) (5,4) (21,13) (6,1) (18,11) (17,13) (12,17) (23,2) (12,4) (18,1) (8,20) (1,9) (14,3) (24,7) (13,1) (15,1) (20,2) (2,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1033",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,25) (1,0) (14,3) (17,2) (24,22) (18,12) (16,15) (17,1) (25,18) (11,16) (21,16) (4,2) (24,7) (6,5) (0,14) (14,9) (10,14) (5,23) (20,19) (19,25) (3,5) (20,15) (6,13) (14,8) (9,4) (17,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1043",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,24) (8,21) (0,1) (2,10) (24,16) (13,8) (9,13) (17,16) (0,17) (18,14) (25,3) (0,3) (9,4) (10,4) (23,1) (25,19) (25,11) (6,4) (24,5) (20,11) (24,18) (22,23) (15,1) (20,8) (22,18) (0,2) (23,7) (10,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph730",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,29) (29,9) (8,0) (9,14) (4,12) (27,0) (0,1) (10,24) (18,21) (20,3) (13,22) (5,25) (28,14) (5,30) (1,32) (20,5) (16,6) (3,29) (22,11) (17,25) (26,16) (17,21) (31,4) (9,15) (7,8) (21,19) (4,23) (4,26) (2,5) (8,21) (30,26) (13,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1039",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,0) (14,15) (2,7) (0,4) (0,3) (23,11) (19,18) (21,8) (6,14) (3,18) (0,6) (2,10) (4,13) (13,1) (11,1) (1,0) (17,15) (25,20) (12,13) (4,25) (1,5) (7,23) (10,15) (22,5) (8,20) (1,9) (15,16) (0,2) (24,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1737",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,21) (31,4) (17,7) (5,32) (9,16) (10,3) (21,18) (31,0) (22,23) (4,3) (8,7) (9,11) (0,1) (15,22) (2,7) (10,6) (13,30) (18,28) (7,4) (10,27) (4,30) (5,12) (0,2) (13,25) (19,10) (18,29) (26,14) (14,30) (11,25) (22,1) (6,5) (25,23) (24,7) (20,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1023",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,10) (10,24) (4,0) (13,16) (25,2) (16,9) (6,1) (11,18) (2,23) (7,12) (14,4) (2,3) (17,4) (3,0) (5,12) (17,9) (1,0) (2,0) (21,1) (20,7) (25,19) (18,17) (8,18) (1,20) (0,22) (25,16) (18,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph791",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,26) (17,22) (3,8) (31,6) (17,28) (32,30) (20,3) (10,32) (23,1) (21,14) (14,9) (13,8) (16,20) (1,8) (4,2) (20,21) (28,7) (0,29) (26,3) (24,12) (29,9) (15,2) (20,11) (18,5) (3,25) (22,18) (7,16) (9,19) (10,19) (15,13) (29,12) (27,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph489",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,12) (20,2) (25,8) (20,6) (4,25) (1,27) (0,22) (6,25) (0,15) (24,2) (5,17) (27,13) (17,10) (11,25) (23,16) (6,19) (16,7) (3,24) (1,18) (9,23) (19,0) (4,21) (26,8) (29,20) (18,23) (14,4) (17,15) (20,28) (19,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1611",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,5) (1,4) (15,14) (27,19) (25,1) (7,17) (3,7) (10,27) (21,27) (0,3) (13,9) (2,20) (6,8) (30,17) (14,26) (5,18) (24,14) (0,29) (10,0) (22,5) (13,21) (26,12) (0,1) (23,13) (2,1) (16,8) (6,21) (9,17) (2,0) (15,11) (5,31) (28,17) (14,28) (1,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph522",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,8) (6,16) (25,30) (17,15) (4,9) (21,25) (3,24) (28,18) (15,26) (30,8) (28,6) (30,19) (11,15) (20,12) (12,29) (5,24) (18,11) (16,4) (16,14) (24,4) (12,2) (0,27) (19,3) (1,13) (26,22) (13,10) (23,9) (7,28) (29,27) (9,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph85",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,3) (20,6) (15,19) (8,12) (9,23) (5,22) (19,1) (2,0) (13,7) (5,14) (9,1) (19,16) (24,4) (14,24) (5,3) (1,5) (10,14) (13,15) (13,11) (21,20) (8,18) (25,21) (17,13) (6,8) (2,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph733",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,18) (10,2) (0,28) (11,27) (7,3) (31,20) (6,31) (0,23) (15,25) (13,17) (0,30) (29,19) (32,14) (25,31) (2,18) (23,9) (1,4) (26,8) (10,25) (6,7) (9,10) (11,22) (26,4) (15,19) (2,13) (28,14) (28,26) (27,16) (7,11) (17,12) (17,21) (29,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1367",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,22) (2,26) (8,20) (16,18) (23,8) (28,9) (1,0) (19,5) (18,1) (7,28) (20,5) (27,5) (24,0) (0,2) (5,21) (25,3) (6,2) (16,15) (13,9) (11,5) (27,15) (10,7) (0,16) (0,3) (15,26) (24,28) (4,5) (21,14) (14,12) (0,4) (11,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph187",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,17) (9,21) (12,15) (0,3) (13,8) (18,9) (8,23) (19,18) (15,2) (22,16) (12,16) (24,0) (1,8) (16,7) (14,5) (14,3) (15,10) (24,25) (20,5) (14,6) (11,17) (6,16) (3,4) (2,18) (0,13) (13,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1147",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,4) (3,0) (16,12) (2,24) (21,13) (21,11) (2,0) (10,22) (0,1) (17,21) (20,26) (8,25) (0,4) (23,1) (16,15) (15,8) (2,10) (8,24) (19,22) (13,5) (0,14) (15,23) (1,7) (22,3) (18,21) (3,11) (6,14) (14,21) (24,9) (23,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph661",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,17) (13,2) (23,27) (18,23) (5,3) (29,0) (0,23) (5,26) (30,0) (28,2) (7,5) (2,8) (14,1) (24,16) (18,24) (26,13) (12,6) (29,6) (27,25) (1,20) (22,4) (9,21) (11,28) (3,9) (18,15) (28,19) (14,4) (10,23) (26,4) (31,20) (23,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1999",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,2) (10,6) (27,10) (22,1) (10,19) (13,25) (4,30) (18,34) (5,6) (0,31) (17,7) (3,4) (0,1) (3,0) (29,18) (11,25) (9,16) (2,0) (4,32) (5,18) (15,22) (21,13) (24,7) (9,11) (2,20) (5,33) (18,28) (10,3) (13,30) (14,30) (14,26) (8,7) (12,5) (25,23) (21,31) (23,22) (7,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1921",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,8) (32,11) (33,21) (10,31) (3,18) (5,34) (27,12) (23,31) (14,24) (6,21) (20,9) (9,30) (3,8) (6,15) (32,26) (17,34) (19,10) (1,0) (4,1) (30,27) (4,27) (18,21) (28,9) (12,16) (32,25) (8,4) (13,14) (13,1) (29,13) (10,8) (17,15) (6,22) (0,20) (32,31) (7,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph687",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,21) (25,0) (24,29) (23,28) (14,21) (31,23) (19,9) (9,1) (12,14) (23,14) (18,5) (20,1) (4,2) (3,11) (19,10) (11,8) (24,13) (20,5) (22,15) (6,22) (17,16) (1,26) (15,30) (29,14) (28,0) (27,4) (7,23) (4,18) (17,22) (22,31) (16,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph974",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,31) (11,14) (7,22) (1,24) (28,9) (10,32) (3,5) (21,6) (22,17) (13,34) (17,6) (27,32) (24,3) (33,9) (20,24) (21,26) (33,13) (22,0) (23,14) (19,25) (16,23) (1,8) (15,4) (33,2) (12,1) (18,19) (6,29) (9,0) (18,24) (10,19) (20,13) (5,30) (27,4) (16,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph583",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,14) (9,16) (2,25) (24,22) (21,17) (0,24) (7,1) (22,27) (6,12) (8,11) (3,11) (0,11) (13,1) (1,12) (30,25) (25,20) (11,28) (23,9) (23,15) (10,13) (2,17) (24,29) (29,15) (18,4) (24,25) (18,26) (20,1) (6,26) (19,21) (5,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph26",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,9) (16,25) (15,11) (12,2) (12,1) (16,6) (3,18) (19,25) (8,15) (23,6) (10,20) (14,24) (7,9) (8,1) (23,21) (24,19) (5,0) (22,3) (20,18) (6,0) (4,24) (13,17) (1,9) (13,3) (18,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph367",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,18) (1,24) (16,11) (23,4) (9,5) (7,26) (17,26) (11,4) (22,15) (12,13) (6,8) (9,13) (27,0) (14,19) (3,0) (16,12) (9,18) (10,28) (15,28) (7,19) (0,25) (14,28) (3,2) (23,6) (8,14) (2,20) (2,22) (21,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph953",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (5,17) (7,3) (23,9) (5,26) (4,32) (10,27) (29,1) (29,22) (6,24) (10,29) (16,8) (27,28) (26,14) (13,34) (18,13) (7,8) (30,28) (18,6) (11,19) (10,31) (0,11) (14,33) (13,17) (2,24) (25,21) (17,12) (32,8) (10,15) (5,23) (32,20) (21,2) (24,4) (3,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1863",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,18) (12,14) (1,14) (8,7) (6,0) (18,2) (7,14) (16,0) (19,27) (20,17) (0,2) (21,18) (7,32) (24,11) (20,25) (9,11) (28,22) (3,26) (21,29) (25,24) (10,30) (33,2) (26,32) (1,0) (19,24) (4,6) (5,33) (0,3) (18,6) (31,4) (15,1) (4,22) (10,23) (10,7) (6,20) (17,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1487",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (9,1) (26,7) (4,24) (27,12) (13,3) (13,24) (6,0) (15,17) (27,28) (9,14) (1,15) (29,26) (3,18) (26,23) (20,24) (27,19) (0,1) (1,8) (0,2) (18,21) (11,0) (18,9) (23,21) (3,27) (10,26) (8,22) (29,5) (20,16) (25,18) (6,29) (2,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph998",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,21) (13,2) (12,14) (11,10) (29,22) (10,25) (31,26) (4,19) (5,30) (1,7) (28,0) (11,6) (3,24) (5,15) (31,19) (18,9) (13,8) (9,17) (33,1) (23,2) (34,4) (27,28) (7,24) (10,16) (0,18) (23,33) (21,4) (10,12) (20,13) (34,32) (20,10) (28,19) (31,29) (5,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1527",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,4) (18,10) (15,28) (14,18) (26,9) (6,0) (12,18) (8,9) (18,28) (7,21) (9,13) (15,8) (28,19) (0,3) (2,0) (17,23) (5,2) (24,25) (26,27) (16,20) (2,17) (15,6) (22,3) (1,4) (25,14) (11,22) (21,20) (29,30) (30,20) (21,1) (11,2) (1,0) (8,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1035",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,12) (21,20) (22,11) (4,7) (24,15) (10,6) (4,9) (22,15) (13,1) (2,4) (12,8) (25,12) (1,2) (12,19) (5,11) (16,6) (15,18) (14,0) (17,16) (6,18) (0,1) (25,7) (14,23) (12,14) (2,0) (0,3) (0,20) (3,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph513",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (16,30) (15,10) (20,0) (14,0) (6,28) (4,23) (1,17) (30,7) (13,26) (13,19) (1,3) (5,26) (17,12) (21,1) (25,13) (1,29) (0,7) (2,8) (23,8) (16,9) (5,4) (27,15) (30,5) (11,18) (11,27) (14,12) (25,24) (11,14) (20,28) (22,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1269",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,19) (4,20) (22,24) (14,8) (7,23) (7,17) (27,11) (11,10) (2,11) (2,4) (6,0) (23,15) (15,13) (5,9) (6,3) (16,7) (13,5) (22,18) (12,19) (1,4) (1,0) (9,25) (26,15) (22,26) (0,2) (3,23) (0,21) (11,22) (14,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph803",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,32) (4,9) (31,21) (26,6) (15,0) (23,1) (32,17) (0,22) (16,13) (10,18) (14,30) (7,31) (30,12) (5,33) (7,23) (4,25) (2,28) (26,27) (3,10) (33,19) (29,14) (13,30) (20,15) (24,27) (28,26) (14,2) (18,11) (8,26) (1,9) (21,2) (5,9) (0,23) (32,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph573",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,11) (3,7) (20,23) (2,1) (8,30) (0,14) (4,10) (26,12) (14,25) (12,2) (28,26) (17,1) (16,6) (15,30) (9,12) (2,15) (14,12) (15,24) (19,4) (22,13) (18,29) (6,11) (4,7) (28,6) (6,18) (7,25) (20,0) (21,16) (15,27) (22,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph335",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,21) (27,19) (22,5) (18,11) (19,15) (17,28) (24,13) (17,26) (4,14) (3,14) (1,2) (12,28) (15,22) (25,20) (4,7) (25,18) (12,13) (14,19) (0,23) (16,13) (1,9) (9,21) (22,10) (11,19) (24,6) (0,16) (24,27) (8,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1389",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (23,4) (16,0) (19,4) (22,11) (24,21) (21,9) (25,14) (7,9) (4,1) (20,6) (0,1) (23,24) (3,18) (15,20) (1,20) (26,14) (6,18) (2,0) (28,5) (16,10) (12,1) (2,14) (26,0) (6,28) (28,8) (8,11) (17,21) (16,28) (27,23) (7,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph378",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,14) (7,16) (23,26) (10,20) (10,18) (17,28) (22,28) (23,6) (13,12) (14,3) (25,17) (24,6) (4,0) (17,2) (12,21) (18,23) (5,9) (15,11) (25,15) (15,8) (1,15) (14,19) (7,14) (28,9) (12,28) (1,6) (17,4) (19,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph281",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,19) (10,26) (2,25) (2,7) (11,25) (5,17) (20,11) (18,1) (5,14) (13,23) (22,13) (7,8) (21,17) (22,1) (0,9) (5,19) (4,7) (6,4) (22,15) (8,1) (12,14) (16,3) (0,19) (18,27) (23,3) (20,24) (21,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1028",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (0,13) (25,13) (1,12) (4,5) (20,25) (4,11) (23,0) (17,25) (18,9) (21,2) (15,18) (10,1) (21,5) (8,7) (1,7) (25,24) (4,12) (14,15) (9,6) (3,0) (16,8) (22,2) (10,14) (19,25) (3,9) (20,7) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph490",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (22,29) (20,17) (28,3) (24,12) (11,28) (24,2) (6,28) (8,12) (25,22) (29,15) (17,22) (10,23) (9,26) (8,16) (3,27) (10,28) (14,3) (19,10) (26,7) (13,17) (4,23) (26,15) (6,5) (20,21) (0,11) (24,18) (8,0) (2,26) (4,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1793",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (14,32) (31,20) (26,8) (19,29) (25,10) (0,4) (17,13) (30,0) (15,25) (12,17) (22,11) (23,9) (16,27) (31,25) (0,28) (28,26) (21,17) (0,23) (28,14) (29,5) (9,10) (2,18) (6,31) (10,2) (13,2) (3,7) (24,18) (0,3) (26,4) (11,7) (15,19) (2,0) (4,1) (6,7) (27,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph3",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,7) (1,13) (25,20) (2,7) (19,18) (11,1) (21,8) (3,18) (6,14) (18,0) (22,5) (4,25) (10,2) (6,0) (8,20) (15,10) (9,1) (1,5) (13,4) (13,12) (15,16) (24,16) (14,15) (11,23) (15,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph485",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,3) (19,27) (24,10) (21,13) (1,3) (20,2) (22,9) (6,19) (18,3) (24,8) (10,16) (16,2) (20,12) (14,11) (7,28) (13,25) (4,14) (17,10) (21,26) (22,21) (9,5) (21,23) (12,7) (12,25) (4,26) (6,22) (15,14) (29,0) (8,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph184",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,1) (16,13) (6,1) (10,15) (26,13) (11,14) (1,18) (19,4) (11,5) (12,14) (20,0) (1,17) (8,3) (5,23) (25,21) (24,20) (9,16) (4,5) (11,15) (17,12) (23,8) (22,13) (14,0) (26,2) (7,2) (0,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph924",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (5,27) (30,20) (19,30) (10,25) (1,23) (23,8) (19,34) (32,7) (3,19) (0,1) (33,29) (27,32) (9,15) (29,11) (13,20) (22,4) (29,26) (7,24) (10,26) (4,23) (6,16) (8,21) (28,1) (18,33) (31,6) (18,14) (28,12) (33,31) (24,8) (11,17) (4,2) (29,13) (16,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1859",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (26,8) (33,3) (4,13) (21,5) (10,7) (0,31) (7,32) (2,31) (15,31) (32,19) (30,18) (1,2) (33,8) (33,10) (20,6) (4,11) (12,29) (1,0) (3,22) (17,6) (12,18) (25,23) (23,0) (24,30) (9,19) (16,1) (21,20) (5,28) (28,12) (9,13) (27,0) (14,15) (33,2) (21,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph421",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (25,17) (9,27) (21,0) (27,28) (1,17) (6,8) (7,10) (29,21) (14,4) (2,10) (13,16) (15,14) (24,14) (26,13) (3,11) (7,18) (6,29) (0,1) (7,15) (25,10) (20,9) (9,7) (1,12) (23,26) (19,9) (26,2) (12,5) (22,24) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph982",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,15) (9,18) (17,6) (8,18) (30,22) (8,34) (1,25) (2,34) (27,33) (8,19) (5,29) (31,7) (25,4) (12,13) (24,1) (19,31) (24,16) (1,15) (29,25) (28,10) (34,22) (16,13) (33,10) (0,21) (15,17) (4,32) (1,11) (3,14) (17,7) (3,25) (0,33) (5,20) (26,4) (27,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph407",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,24) (0,15) (15,16) (7,23) (24,15) (20,9) (10,7) (11,3) (13,7) (2,19) (4,11) (8,11) (14,22) (2,17) (4,27) (20,17) (28,26) (25,29) (28,12) (22,10) (18,10) (8,5) (6,2) (21,17) (26,3) (11,10) (7,6) (2,29) (1,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1163",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,11) (2,11) (9,5) (7,23) (4,1) (19,12) (15,13) (9,24) (26,15) (5,13) (0,3) (15,19) (0,6) (22,26) (2,0) (4,2) (0,1) (20,4) (18,22) (25,22) (7,17) (16,7) (0,4) (6,3) (8,14) (0,11) (14,5) (23,22) (3,23) (15,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph787",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,7) (1,13) (13,14) (30,9) (0,20) (32,24) (6,19) (5,19) (28,27) (15,6) (32,23) (1,4) (8,3) (27,4) (8,2) (31,29) (14,22) (30,10) (15,32) (10,8) (18,3) (21,31) (12,27) (18,21) (8,4) (11,12) (31,20) (9,25) (6,21) (17,9) (13,26) (10,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph768",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,10) (27,3) (3,14) (18,23) (16,1) (15,0) (18,25) (26,25) (18,19) (24,32) (12,17) (6,16) (5,23) (6,11) (15,30) (29,11) (17,28) (21,5) (21,24) (9,20) (7,6) (1,13) (9,5) (10,12) (30,13) (8,25) (23,14) (4,22) (2,19) (4,1) (31,32) (17,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph575",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (9,21) (27,10) (6,9) (19,26) (15,18) (0,27) (23,0) (17,1) (7,13) (23,13) (26,3) (29,28) (13,9) (30,14) (22,19) (14,29) (8,5) (30,20) (17,25) (15,11) (5,2) (16,21) (11,30) (30,8) (24,8) (3,4) (26,13) (0,17) (11,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph667",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,17) (15,12) (0,8) (6,12) (23,6) (9,11) (7,10) (2,12) (30,19) (14,5) (13,1) (27,11) (4,31) (17,22) (16,25) (3,8) (0,19) (31,0) (21,11) (2,18) (26,9) (25,11) (29,21) (28,25) (16,10) (23,30) (20,23) (5,17) (7,6) (8,1) (24,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph670",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (7,22) (8,6) (29,9) (18,13) (4,29) (30,26) (3,28) (0,24) (14,27) (19,21) (19,13) (0,31) (11,4) (5,20) (4,26) (4,22) (10,29) (21,16) (25,17) (30,5) (0,8) (17,21) (21,8) (2,16) (14,9) (20,3) (5,25) (1,5) (10,23) (26,15) (9,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1820",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,21) (28,21) (23,17) (4,10) (24,0) (27,23) (25,32) (1,23) (12,27) (0,4) (21,8) (8,7) (16,33) (29,31) (20,5) (30,33) (23,22) (19,6) (30,4) (1,15) (6,31) (5,10) (9,11) (31,3) (3,14) (0,6) (0,2) (13,16) (21,2) (20,15) (1,0) (26,0) (18,9) (3,1) (21,10) (3,0) (17,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph677",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,15) (21,15) (14,19) (25,4) (28,19) (14,23) (19,18) (19,11) (3,12) (26,0) (15,24) (20,28) (26,24) (14,21) (7,29) (4,1) (18,17) (23,2) (31,22) (9,25) (27,5) (29,21) (8,24) (12,10) (3,30) (9,6) (5,21) (6,31) (29,1) (13,26) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph696",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,9) (3,21) (30,15) (19,25) (9,28) (1,28) (18,22) (14,28) (14,24) (29,2) (13,4) (17,18) (21,29) (1,27) (24,5) (15,28) (31,18) (20,22) (22,27) (11,24) (8,26) (10,12) (0,20) (1,7) (19,13) (4,8) (11,19) (21,11) (30,6) (0,16) (23,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1501",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,18) (1,4) (23,20) (27,23) (0,5) (7,8) (28,11) (18,2) (0,16) (13,26) (2,0) (3,0) (16,20) (24,0) (3,10) (10,25) (12,29) (17,2) (15,26) (1,0) (15,30) (14,29) (9,21) (9,28) (13,20) (25,19) (30,6) (22,2) (8,29) (8,17) (25,5) (0,4) (17,11) (5,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1502",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,17) (23,0) (8,23) (23,6) (21,10) (25,3) (27,23) (0,1) (24,29) (27,21) (16,22) (28,11) (13,7) (16,3) (14,10) (20,24) (26,9) (15,13) (22,4) (15,8) (29,12) (26,19) (14,1) (24,25) (2,30) (14,17) (7,18) (19,18) (5,11) (20,17) (30,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1447",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,4) (8,26) (29,3) (20,3) (6,15) (5,13) (27,23) (21,5) (12,6) (18,10) (14,0) (19,4) (20,23) (4,25) (23,9) (21,16) (11,5) (22,2) (2,17) (0,1) (5,6) (0,24) (3,0) (12,7) (0,2) (25,29) (14,28) (24,26) (24,18) (27,14) (1,22) (22,21) (9,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1032",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,25) (6,0) (0,1) (11,20) (9,16) (10,14) (0,5) (22,4) (15,1) (22,14) (3,10) (7,21) (3,7) (24,12) (0,4) (6,2) (19,4) (18,21) (12,8) (0,2) (3,0) (0,17) (5,16) (22,11) (23,13) (7,5) (8,23) (11,8) (25,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph176",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,12) (20,3) (20,13) (5,24) (2,1) (12,11) (18,4) (6,19) (9,15) (11,1) (26,18) (25,12) (16,5) (13,9) (17,10) (10,15) (16,19) (21,12) (26,23) (23,0) (8,0) (22,0) (14,7) (11,19) (20,23) (16,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph467",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,19) (15,13) (22,12) (23,18) (9,15) (26,28) (15,25) (17,25) (29,0) (2,19) (15,1) (10,21) (1,6) (14,17) (4,14) (6,27) (9,8) (6,23) (3,4) (11,28) (17,5) (29,24) (14,7) (12,28) (18,10) (16,12) (23,28) (29,2) (7,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1167",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,2) (17,18) (20,7) (22,21) (0,2) (16,2) (24,26) (17,21) (10,11) (7,9) (24,14) (12,22) (4,11) (2,26) (10,15) (17,2) (15,0) (7,6) (3,0) (20,8) (8,1) (15,13) (19,10) (0,1) (5,11) (3,25) (11,3) (7,10) (4,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1416",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (10,0) (10,3) (22,27) (16,5) (6,19) (29,11) (14,26) (20,8) (2,0) (2,6) (14,24) (2,8) (16,22) (3,0) (26,15) (12,8) (7,19) (6,18) (29,4) (11,16) (26,28) (0,1) (0,26) (4,13) (25,0) (19,1) (24,4) (17,24) (23,1) (16,21) (9,25) (16,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1741",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,25) (13,31) (6,7) (15,12) (10,7) (17,24) (17,22) (11,21) (2,18) (20,23) (19,30) (8,1) (25,28) (25,11) (9,26) (17,5) (1,0) (32,16) (29,21) (12,6) (12,2) (32,19) (1,14) (10,31) (23,30) (23,24) (32,3) (6,23) (5,0) (0,8) (8,4) (11,27) (11,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1994",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,5) (17,12) (1,0) (2,6) (9,30) (33,18) (5,30) (2,8) (6,24) (7,16) (2,12) (27,21) (1,17) (6,18) (0,9) (27,31) (3,5) (10,0) (14,1) (0,2) (16,26) (3,0) (34,22) (15,31) (32,12) (25,12) (13,20) (31,4) (5,21) (16,29) (11,23) (26,23) (4,0) (19,26) (20,34) (34,12) (28,16) (6,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph409",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,12) (17,21) (26,23) (13,23) (0,24) (6,9) (2,13) (3,29) (12,7) (24,5) (3,22) (8,27) (10,25) (20,27) (1,16) (19,17) (9,5) (16,25) (16,28) (8,21) (14,11) (10,20) (18,22) (7,0) (15,22) (9,11) (8,13) (4,25) (29,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph55",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,14) (16,8) (0,23) (25,17) (22,2) (20,25) (13,25) (21,2) (3,9) (21,5) (8,7) (4,11) (15,14) (24,25) (5,4) (9,6) (4,12) (1,10) (0,13) (18,9) (1,12) (18,15) (20,7) (7,1) (19,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1075",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,8) (3,0) (0,1) (13,3) (12,23) (10,19) (13,4) (22,15) (10,11) (22,10) (17,1) (24,7) (19,1) (9,25) (21,20) (19,23) (2,0) (16,14) (14,11) (23,9) (13,6) (20,0) (22,8) (18,11) (11,2) (3,2) (5,18) (5,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph969",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,18) (34,9) (25,3) (24,26) (4,28) (20,32) (10,25) (4,15) (3,11) (17,6) (5,22) (7,34) (27,3) (6,23) (1,9) (30,14) (0,20) (26,18) (8,2) (2,13) (19,3) (16,34) (5,27) (9,26) (14,2) (7,29) (4,12) (13,21) (32,25) (15,5) (7,33) (14,3) (27,23) (3,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph871",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,10) (15,17) (28,13) (16,10) (14,23) (20,6) (6,15) (19,5) (30,31) (13,1) (27,12) (3,8) (30,9) (32,25) (4,8) (19,9) (10,8) (17,33) (24,32) (13,14) (4,1) (11,12) (31,22) (3,18) (32,7) (0,20) (6,21) (2,8) (27,29) (9,26) (21,18) (27,4) (32,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1695",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,0) (18,7) (25,4) (6,22) (27,16) (1,0) (8,4) (3,0) (10,29) (19,2) (12,7) (6,24) (11,22) (2,13) (19,20) (25,30) (26,27) (26,22) (28,4) (17,6) (11,20) (10,12) (19,5) (24,1) (15,2) (4,29) (22,12) (21,30) (9,30) (23,6) (8,31) (2,0) (14,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1796",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,24) (0,1) (19,30) (4,11) (31,5) (8,6) (9,30) (15,27) (26,3) (0,15) (16,32) (20,22) (14,25) (10,22) (24,0) (27,7) (13,23) (4,23) (6,30) (14,5) (28,9) (17,20) (21,19) (17,21) (9,1) (6,16) (32,23) (1,31) (10,2) (27,29) (18,2) (26,25) (12,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph899",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,10) (2,17) (7,9) (20,1) (18,21) (17,10) (30,13) (29,9) (33,6) (10,22) (27,23) (11,32) (7,30) (16,4) (29,4) (26,2) (15,10) (14,11) (5,33) (12,6) (1,10) (3,2) (10,28) (27,4) (25,30) (26,0) (10,11) (3,19) (31,14) (33,14) (26,24) (23,26) (8,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph943",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,9) (13,16) (30,12) (23,7) (21,2) (10,18) (4,25) (18,11) (5,9) (3,10) (14,2) (24,27) (23,0) (13,30) (27,26) (32,11) (34,5) (32,17) (14,30) (31,7) (15,20) (33,31) (8,26) (2,28) (1,23) (34,21) (26,28) (29,14) (22,0) (19,33) (1,9) (6,26) (32,27) (15,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph97",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,16) (2,6) (6,13) (19,9) (22,13) (4,12) (20,13) (4,24) (17,10) (5,20) (6,8) (25,22) (21,19) (1,23) (17,15) (11,1) (7,24) (24,14) (18,21) (0,23) (15,1) (23,13) (3,21) (19,16) (7,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph438",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,11) (27,26) (6,0) (11,8) (2,5) (22,11) (14,25) (21,20) (20,29) (8,9) (6,15) (23,17) (9,26) (8,15) (18,12) (14,18) (25,24) (28,19) (3,22) (7,21) (17,2) (28,15) (18,28) (4,23) (4,1) (20,16) (13,9) (18,10) (1,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph749",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,5) (6,31) (20,11) (20,16) (0,29) (3,20) (12,24) (14,21) (29,12) (8,13) (1,23) (29,9) (10,19) (26,6) (25,3) (21,20) (32,10) (19,9) (18,22) (15,13) (2,15) (16,7) (26,3) (9,14) (28,7) (28,17) (17,22) (4,2) (3,8) (8,1) (11,27) (32,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1400",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,25) (16,21) (26,10) (1,11) (14,0) (6,13) (13,15) (28,26) (27,9) (2,15) (9,24) (20,7) (20,22) (9,0) (21,10) (23,19) (25,0) (5,9) (14,12) (19,9) (15,3) (0,7) (21,4) (7,11) (7,8) (22,17) (18,8) (23,4) (27,13) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1993",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,5) (10,31) (29,23) (16,0) (4,20) (10,2) (1,15) (24,32) (21,32) (14,12) (19,3) (9,12) (22,8) (28,6) (15,9) (12,3) (3,0) (20,27) (17,16) (1,25) (26,33) (5,16) (8,29) (1,6) (11,0) (24,12) (20,33) (1,0) (18,32) (1,22) (34,9) (7,32) (0,2) (2,22) (9,13) (4,0) (23,30) (28,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph547",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,6) (25,6) (21,30) (5,18) (28,11) (29,13) (7,26) (19,4) (23,26) (14,8) (4,21) (17,30) (0,24) (8,0) (27,13) (20,18) (15,2) (1,0) (10,24) (15,18) (10,11) (15,8) (3,25) (9,2) (24,12) (17,29) (16,1) (27,23) (24,22) (25,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph553",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,22) (24,8) (16,18) (1,7) (17,26) (2,18) (12,15) (4,9) (20,27) (13,15) (15,23) (17,5) (17,15) (29,10) (27,30) (15,22) (26,29) (26,21) (17,8) (18,3) (0,19) (0,29) (25,7) (28,17) (20,14) (2,19) (12,20) (7,6) (11,19) (11,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph711",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (19,7) (27,4) (5,12) (22,10) (24,0) (32,14) (12,22) (7,22) (26,8) (14,29) (25,28) (0,20) (14,6) (24,9) (6,2) (11,29) (29,17) (1,12) (8,30) (23,30) (7,26) (18,27) (28,14) (14,13) (24,15) (3,20) (31,14) (30,27) (32,9) (14,16) (21,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph33",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,22) (13,25) (23,12) (4,19) (6,19) (5,4) (14,17) (16,20) (1,3) (5,11) (19,9) (10,22) (8,17) (24,14) (5,12) (24,6) (21,6) (20,6) (0,6) (15,7) (3,4) (13,18) (4,7) (13,0) (23,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph294",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,18) (24,7) (26,4) (20,18) (15,9) (21,26) (4,14) (27,10) (12,8) (10,2) (5,6) (23,4) (24,19) (12,27) (17,23) (12,5) (13,22) (10,23) (14,0) (1,12) (11,18) (21,7) (3,7) (24,22) (8,16) (0,25) (17,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1242",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,5) (17,22) (0,1) (7,11) (24,12) (23,8) (26,13) (18,19) (16,21) (0,3) (4,24) (13,23) (15,6) (18,6) (19,23) (4,0) (2,17) (6,3) (12,16) (9,19) (4,7) (6,27) (2,14) (1,12) (2,19) (0,2) (25,15) (5,10) (12,0) (21,22) (20,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph985",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,32) (29,21) (2,32) (23,17) (22,33) (7,28) (10,12) (22,13) (10,25) (5,7) (7,3) (11,13) (20,4) (16,27) (19,7) (32,33) (6,19) (0,12) (16,17) (15,17) (28,9) (32,1) (28,24) (15,26) (20,29) (8,2) (9,26) (17,20) (31,0) (14,8) (10,34) (14,28) (0,27) (11,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1375",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,9) (12,8) (16,19) (1,0) (2,28) (18,6) (18,15) (26,12) (10,6) (4,7) (7,3) (6,16) (15,23) (6,28) (7,25) (12,21) (5,11) (25,15) (0,14) (14,24) (12,14) (1,2) (4,17) (2,12) (1,13) (20,22) (22,11) (27,26) (0,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1906",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,2) (8,24) (31,32) (22,18) (16,7) (33,32) (6,33) (2,15) (30,9) (1,33) (26,6) (1,0) (7,29) (4,33) (20,16) (3,27) (25,12) (17,28) (15,13) (20,3) (34,19) (20,21) (9,19) (8,13) (26,3) (14,9) (28,11) (23,1) (10,18) (29,12) (17,22) (14,21) (20,11) (0,29) (3,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph224",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,10) (5,26) (16,8) (0,7) (9,22) (4,23) (3,24) (25,6) (18,27) (2,20) (4,27) (19,14) (4,8) (2,10) (14,5) (22,21) (24,13) (1,2) (21,10) (18,2) (17,11) (9,6) (27,7) (22,15) (0,19) (12,19) (27,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1031",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,10) (6,25) (13,9) (10,20) (22,18) (1,0) (15,1) (2,11) (21,15) (16,22) (12,14) (23,11) (25,17) (20,0) (17,4) (6,7) (2,12) (5,24) (10,9) (10,14) (5,3) (0,16) (25,22) (0,19) (15,11) (10,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1292",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,22) (2,25) (5,8) (23,22) (27,25) (23,9) (19,3) (4,12) (19,15) (22,13) (18,21) (11,5) (0,3) (7,12) (1,0) (6,23) (0,22) (14,17) (0,4) (2,1) (20,0) (19,4) (2,0) (7,10) (4,20) (16,11) (17,22) (26,10) (11,9) (25,22) (19,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph640",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,10) (20,29) (2,24) (14,26) (11,19) (29,28) (9,23) (7,8) (5,26) (13,18) (28,27) (27,10) (10,25) (24,6) (31,17) (21,2) (4,24) (18,6) (5,17) (3,7) (29,1) (0,21) (8,4) (12,17) (22,5) (10,15) (21,23) (0,11) (14,13) (3,15) (16,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1046",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,20) (3,0) (19,25) (0,5) (16,11) (3,10) (20,1) (8,4) (22,23) (1,13) (24,21) (13,5) (21,15) (0,4) (23,1) (4,14) (16,7) (23,14) (17,16) (11,2) (7,19) (6,3) (24,8) (2,0) (24,9) (0,1) (18,1) (10,17) (25,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph983",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,1) (33,11) (5,4) (2,12) (23,2) (27,7) (34,21) (6,21) (10,21) (20,19) (0,1) (8,19) (29,9) (14,3) (28,23) (7,6) (25,10) (5,6) (31,0) (14,8) (1,15) (11,26) (30,5) (5,32) (31,2) (20,29) (22,34) (33,16) (19,24) (18,31) (17,24) (5,19) (19,16) (12,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1729",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,20) (12,32) (2,0) (9,18) (1,31) (27,28) (4,25) (3,0) (27,30) (15,14) (30,8) (21,10) (21,4) (27,17) (14,21) (20,13) (15,7) (5,11) (31,0) (19,6) (26,21) (22,9) (12,6) (14,0) (29,5) (17,21) (27,6) (23,3) (22,23) (5,4) (12,24) (14,20) (16,5) (2,17) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1178",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,26) (14,23) (5,10) (22,2) (19,22) (24,17) (14,25) (6,11) (23,20) (15,21) (14,0) (4,18) (13,6) (24,0) (16,2) (23,9) (8,18) (5,6) (9,21) (12,5) (25,4) (21,5) (1,22) (26,7) (3,12) (22,24) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1947",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (27,32) (9,11) (5,11) (1,0) (3,0) (24,3) (26,2) (9,6) (14,24) (2,0) (28,16) (34,17) (3,33) (14,5) (25,34) (13,22) (34,12) (1,5) (27,12) (15,30) (18,24) (5,32) (29,14) (20,23) (2,14) (2,16) (19,24) (0,29) (22,25) (27,20) (32,21) (10,19) (30,32) (0,31) (8,5) (4,12) (7,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1719",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,30) (1,4) (5,14) (15,2) (23,27) (22,11) (17,14) (26,29) (22,13) (26,12) (20,3) (9,31) (1,27) (21,20) (3,0) (8,0) (11,16) (3,7) (9,32) (25,19) (8,11) (17,3) (19,28) (25,11) (5,15) (10,7) (16,1) (0,2) (11,12) (0,1) (21,16) (18,20) (19,32) (24,3) (28,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph382",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (12,14) (8,28) (0,20) (24,13) (11,18) (21,1) (16,10) (8,3) (4,22) (23,25) (1,27) (6,1) (14,11) (5,25) (15,16) (0,14) (26,13) (12,17) (0,7) (26,20) (17,1) (4,5) (28,2) (23,9) (19,13) (7,2) (11,5) (15,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1546",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,30) (21,20) (0,2) (6,0) (22,15) (9,4) (17,10) (2,3) (5,16) (3,30) (24,6) (23,6) (23,8) (0,13) (12,27) (14,24) (6,19) (4,28) (5,12) (1,3) (18,4) (6,29) (19,11) (5,26) (14,20) (1,0) (17,7) (3,0) (22,13) (4,19) (13,7) (25,4) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1917",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (33,21) (6,21) (34,5) (8,4) (0,1) (9,20) (9,30) (2,0) (3,8) (11,32) (13,1) (32,25) (18,3) (4,27) (14,24) (27,12) (32,26) (13,14) (10,8) (0,4) (1,4) (18,21) (15,17) (31,32) (22,6) (0,3) (15,6) (28,9) (19,7) (34,17) (10,31) (29,13) (27,30) (10,19) (23,31) (20,0) (8,2) (12,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph891",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,27) (7,32) (30,23) (33,15) (29,23) (22,8) (10,31) (3,12) (16,5) (12,9) (20,9) (1,15) (18,32) (29,8) (4,20) (27,28) (22,2) (1,6) (6,28) (10,2) (19,3) (16,17) (26,33) (11,0) (25,1) (32,21) (24,12) (32,24) (5,12) (1,22) (13,9) (12,14) (16,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph280",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,20) (6,16) (22,25) (1,21) (19,1) (12,8) (19,7) (14,26) (14,24) (8,18) (0,23) (11,26) (4,26) (16,11) (6,17) (0,10) (2,8) (6,2) (19,6) (25,9) (5,16) (15,24) (16,22) (10,3) (0,26) (13,4) (24,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph638",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,25) (8,5) (21,5) (17,0) (20,30) (26,12) (22,12) (11,21) (9,29) (6,11) (27,23) (2,17) (24,13) (24,23) (25,20) (30,5) (0,31) (15,16) (8,14) (5,29) (15,10) (18,5) (14,7) (1,25) (16,24) (13,9) (28,11) (13,26) (24,3) (31,19) (4,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1486",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,10) (2,0) (22,16) (19,11) (18,23) (0,4) (7,15) (23,16) (16,1) (9,4) (10,27) (10,26) (28,12) (8,6) (17,0) (28,15) (1,0) (28,22) (24,25) (2,5) (1,20) (26,1) (24,17) (29,25) (6,4) (0,19) (0,3) (29,2) (3,21) (22,9) (7,13) (11,15) (14,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph591",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (25,13) (9,5) (7,28) (8,24) (10,17) (9,22) (15,14) (29,0) (3,4) (14,11) (21,22) (21,13) (27,19) (2,20) (2,16) (10,16) (21,26) (4,14) (12,8) (4,26) (12,25) (6,19) (23,21) (29,20) (24,10) (18,3) (3,1) (12,7) (12,30) (22,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1827",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,23) (0,26) (7,29) (24,8) (31,22) (15,5) (29,21) (14,23) (13,26) (31,3) (15,6) (28,20) (17,18) (9,6) (18,19) (4,0) (0,3) (3,12) (1,29) (5,33) (25,4) (19,14) (26,24) (21,32) (16,15) (12,10) (30,19) (19,11) (0,1) (25,9) (27,5) (4,1) (24,15) (21,14) (5,0) (28,21) (2,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1792",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,2) (25,30) (7,25) (26,1) (29,25) (25,13) (5,12) (11,6) (2,0) (29,1) (2,6) (17,20) (3,0) (13,18) (12,17) (27,8) (0,1) (5,1) (12,14) (23,28) (9,21) (1,15) (22,26) (18,8) (4,11) (16,14) (0,4) (32,27) (9,5) (12,24) (3,30) (10,7) (28,5) (19,13) (0,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph588",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,23) (10,0) (19,2) (18,9) (25,28) (21,25) (2,16) (0,3) (9,24) (27,9) (6,13) (3,22) (25,8) (30,3) (27,20) (19,29) (1,28) (11,8) (0,15) (8,5) (15,17) (9,13) (1,20) (23,30) (2,12) (2,4) (8,4) (15,7) (23,26) (10,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1347",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,27) (7,21) (9,5) (26,2) (1,0) (22,2) (21,27) (14,0) (21,11) (9,6) (9,20) (2,16) (4,28) (14,12) (19,1) (12,23) (21,17) (2,13) (7,1) (19,23) (6,18) (27,26) (3,0) (15,8) (3,14) (23,25) (2,0) (9,26) (15,2) (8,10) (24,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph158",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,12) (4,5) (21,25) (4,19) (1,25) (26,2) (11,5) (22,13) (9,16) (18,1) (20,0) (5,23) (26,13) (1,6) (15,10) (1,17) (11,14) (12,17) (8,3) (20,24) (14,0) (15,11) (8,23) (13,16) (7,0) (7,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph126",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,8) (2,23) (7,11) (24,10) (16,4) (25,16) (25,0) (2,8) (19,1) (5,13) (3,26) (21,0) (8,4) (18,24) (20,13) (10,11) (9,10) (26,0) (3,6) (1,22) (10,20) (17,10) (12,15) (14,21) (6,12) (22,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph901",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (10,21) (20,13) (31,15) (18,33) (29,22) (1,27) (2,31) (26,10) (19,4) (11,23) (18,21) (28,20) (13,6) (3,11) (27,9) (25,8) (11,34) (0,32) (16,22) (12,18) (11,5) (22,17) (25,18) (8,9) (24,21) (31,21) (30,5) (7,20) (14,1) (23,20) (29,0) (28,21) (4,25) (1,32)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1328",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,7) (12,11) (9,13) (4,18) (8,0) (12,26) (25,23) (28,21) (16,7) (26,18) (24,0) (10,15) (5,23) (6,19) (1,2) (19,16) (28,27) (0,1) (22,12) (9,15) (12,3) (5,16) (20,13) (1,11) (27,0) (28,20) (19,11) (20,3) (2,0) (17,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1696",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,3) (4,24) (5,9) (31,16) (7,26) (9,6) (10,31) (17,11) (1,27) (3,4) (6,14) (12,29) (11,24) (3,31) (20,27) (22,11) (1,0) (6,25) (27,9) (0,2) (18,2) (7,24) (23,19) (28,8) (29,17) (1,18) (6,10) (24,8) (29,15) (25,21) (0,3) (3,30) (13,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1218",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,11) (24,25) (24,27) (3,14) (13,8) (16,7) (1,8) (9,18) (0,3) (20,5) (12,16) (22,16) (2,0) (3,4) (5,14) (15,12) (17,11) (13,0) (27,17) (1,0) (4,0) (26,0) (16,6) (21,9) (6,14) (8,23) (18,19) (15,2) (15,10) (2,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph365",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,0) (13,11) (12,3) (10,27) (26,24) (23,17) (16,18) (22,9) (28,8) (25,12) (5,7) (15,11) (14,13) (27,19) (26,7) (1,19) (6,17) (8,2) (0,4) (12,21) (28,4) (16,5) (12,7) (0,18) (17,20) (24,17) (11,22) (12,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph372",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,19) (10,26) (18,10) (21,15) (8,16) (17,4) (14,12) (14,6) (8,22) (11,19) (6,20) (23,27) (0,9) (14,16) (2,23) (17,25) (1,15) (12,28) (1,7) (23,11) (21,13) (27,15) (0,16) (17,24) (24,26) (5,24) (24,22) (3,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph351",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,28) (10,28) (9,5) (22,15) (14,19) (12,13) (24,1) (0,3) (4,23) (19,7) (15,28) (18,24) (0,25) (8,6) (2,3) (22,2) (14,8) (26,17) (26,7) (21,0) (12,16) (16,11) (11,4) (23,6) (13,9) (20,2) (0,27) (18,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph905",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,8) (10,23) (11,34) (34,30) (21,13) (7,33) (31,13) (12,9) (16,32) (26,2) (25,8) (0,33) (17,22) (32,30) (24,26) (34,9) (15,1) (4,7) (8,3) (6,19) (28,20) (29,3) (25,20) (7,17) (21,34) (16,27) (19,26) (18,14) (5,32) (1,23) (18,11) (24,15) (26,5) (4,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph257",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (27,14) (24,0) (20,19) (8,10) (27,24) (0,11) (17,16) (26,22) (13,26) (3,16) (26,7) (23,10) (13,14) (26,9) (24,4) (2,15) (2,22) (23,21) (16,25) (5,0) (12,23) (6,17) (9,20) (12,3) (3,26) (18,23) (1,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph603",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,13) (16,26) (31,12) (29,18) (7,27) (15,10) (11,14) (28,10) (15,12) (21,31) (19,16) (12,6) (12,23) (31,8) (4,21) (29,23) (13,30) (25,12) (16,24) (28,3) (22,18) (30,17) (11,15) (7,2) (9,31) (11,20) (1,11) (20,7) (0,16) (5,15) (21,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph505",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,12) (16,15) (11,18) (0,26) (28,3) (25,2) (2,27) (12,27) (4,17) (17,18) (28,1) (19,18) (7,14) (7,20) (22,25) (16,4) (10,20) (29,30) (0,4) (2,5) (25,10) (1,26) (26,20) (24,0) (23,1) (29,17) (18,9) (21,30) (28,13) (8,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph766",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (11,30) (26,1) (21,13) (29,18) (11,32) (9,25) (12,25) (2,7) (6,26) (3,8) (0,12) (31,17) (10,8) (12,24) (0,32) (9,13) (6,4) (26,20) (15,29) (16,8) (12,8) (27,1) (28,14) (4,15) (5,11) (28,8) (26,19) (10,23) (8,20) (22,13) (14,17) (14,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1795",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,30) (0,1) (3,0) (25,3) (6,31) (14,9) (10,32) (15,2) (0,29) (1,8) (28,17) (18,5) (3,8) (13,15) (28,7) (19,10) (13,8) (26,6) (16,7) (20,16) (29,9) (11,27) (21,14) (1,23) (3,20) (0,2) (11,20) (12,24) (22,17) (26,3) (22,18) (29,12) (19,9) (4,2) (20,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1037",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (15,21) (13,15) (2,11) (10,11) (6,3) (1,4) (15,22) (20,4) (7,16) (1,0) (7,17) (23,7) (9,24) (5,14) (19,12) (14,8) (25,22) (23,3) (22,18) (2,4) (6,0) (13,5) (0,11) (5,9) (15,19) (23,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph172",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,1) (12,5) (1,6) (0,25) (8,18) (22,2) (2,25) (4,0) (14,4) (1,26) (17,16) (23,10) (25,18) (10,20) (7,20) (1,19) (18,15) (0,21) (18,11) (7,12) (9,17) (17,4) (20,26) (13,16) (3,2) (26,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1397",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,2) (4,27) (2,0) (12,23) (21,7) (4,28) (8,10) (18,6) (21,27) (2,26) (3,0) (16,2) (14,0) (8,15) (0,1) (21,11) (22,2) (9,26) (14,3) (24,20) (23,25) (23,19) (1,7) (9,20) (15,2) (1,19) (26,27) (17,21) (12,14) (6,9) (5,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1976",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,26) (19,18) (27,5) (15,16) (9,6) (28,19) (19,14) (29,1) (0,26) (1,4) (19,11) (2,23) (22,31) (28,20) (21,5) (10,12) (3,31) (34,21) (30,34) (3,12) (15,34) (23,14) (3,0) (24,8) (32,21) (14,21) (0,1) (29,7) (4,25) (15,24) (0,2) (25,9) (18,17) (33,29) (6,15) (24,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1574",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,8) (18,7) (20,25) (6,0) (11,25) (15,23) (22,24) (4,21) (16,1) (0,19) (28,1) (0,1) (23,21) (14,10) (0,3) (4,27) (10,3) (5,17) (7,11) (11,22) (2,30) (12,29) (7,30) (9,6) (0,2) (0,4) (22,14) (11,8) (16,13) (3,27) (8,12) (29,5) (26,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph443",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,24) (22,11) (17,23) (17,6) (12,7) (13,11) (5,7) (9,22) (27,7) (12,25) (2,8) (19,1) (24,17) (0,18) (14,13) (26,29) (15,11) (27,10) (8,28) (5,16) (18,16) (17,20) (11,0) (12,21) (4,0) (1,12) (12,3) (4,29) (19,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph493",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,11) (24,5) (16,7) (29,6) (7,1) (0,12) (4,15) (25,9) (1,27) (23,9) (7,10) (13,9) (20,15) (24,25) (17,16) (19,12) (12,17) (14,3) (3,8) (24,28) (26,3) (11,17) (26,5) (23,18) (21,2) (29,22) (4,2) (6,8) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph330",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,26) (16,27) (8,2) (5,9) (9,6) (22,21) (23,10) (4,3) (25,12) (23,13) (0,2) (24,20) (15,17) (12,26) (10,12) (16,12) (28,20) (17,13) (14,23) (5,18) (23,4) (9,2) (6,1) (11,2) (17,24) (21,15) (23,11) (19,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1632",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,25) (0,1) (11,29) (20,9) (30,15) (13,1) (14,23) (31,24) (18,25) (5,21) (25,26) (15,0) (0,2) (18,23) (1,4) (6,11) (28,17) (2,19) (30,13) (3,27) (16,17) (17,12) (24,21) (5,9) (16,1) (10,12) (22,4) (3,14) (6,16) (7,6) (10,19) (5,23) (19,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph518",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,8) (24,17) (7,19) (20,8) (6,16) (0,25) (16,22) (6,18) (19,6) (11,30) (24,4) (14,24) (29,28) (22,27) (10,0) (26,29) (16,21) (4,11) (25,9) (11,16) (26,14) (1,19) (2,8) (26,15) (0,26) (2,6) (10,3) (13,4) (16,5) (23,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph316",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,14) (13,17) (5,18) (4,21) (13,27) (4,19) (10,24) (23,27) (12,24) (1,0) (15,25) (9,2) (10,11) (8,0) (3,25) (17,28) (25,6) (23,22) (26,11) (15,18) (21,24) (6,23) (15,8) (16,1) (7,26) (20,18) (24,0) (2,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph70",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,23) (12,6) (7,11) (11,3) (2,25) (18,4) (22,21) (14,9) (20,1) (2,17) (8,13) (19,15) (22,24) (13,15) (0,24) (1,10) (12,1) (9,23) (25,24) (5,1) (6,15) (11,0) (18,17) (25,20) (16,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph614",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,2) (12,17) (13,18) (18,6) (20,29) (21,2) (9,23) (3,15) (4,8) (26,14) (3,7) (5,22) (21,0) (24,4) (10,27) (30,10) (5,17) (28,27) (0,11) (8,7) (21,23) (13,14) (15,10) (26,5) (19,11) (24,6) (29,28) (25,10) (8,16) (1,29) (31,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph88",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,5) (5,3) (2,7) (8,20) (8,21) (22,15) (23,15) (1,18) (13,11) (5,11) (0,24) (12,9) (17,5) (7,14) (24,10) (0,16) (5,20) (6,2) (9,21) (0,3) (5,18) (16,15) (19,0) (14,16) (25,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1641",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,2) (26,6) (1,23) (6,30) (13,8) (26,3) (17,28) (27,11) (10,31) (13,15) (4,0) (0,3) (21,20) (4,2) (14,21) (22,18) (10,19) (29,9) (16,7) (12,24) (29,12) (3,20) (0,29) (20,11) (19,9) (3,25) (16,20) (5,18) (7,28) (22,17) (9,14) (1,8) (3,8) (1,0) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph530",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,28) (26,13) (17,8) (13,18) (2,18) (6,30) (29,14) (19,25) (17,2) (20,13) (20,23) (20,16) (0,24) (15,26) (15,30) (7,8) (1,4) (25,5) (16,0) (29,8) (7,5) (9,21) (2,22) (9,28) (25,10) (17,11) (10,3) (1,0) (12,29) (23,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1221",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,12) (17,7) (24,10) (22,1) (18,19) (13,24) (12,17) (26,4) (8,6) (3,5) (3,10) (19,2) (0,1) (9,14) (27,23) (21,18) (0,6) (7,24) (19,27) (27,14) (11,15) (20,21) (27,25) (17,26) (7,6) (11,18) (24,21) (7,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph809",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,4) (26,33) (24,28) (12,31) (1,15) (0,4) (2,1) (5,7) (12,23) (26,29) (28,27) (14,16) (9,22) (2,6) (21,22) (13,26) (18,22) (31,5) (14,26) (19,27) (32,17) (25,11) (21,26) (28,6) (17,19) (33,30) (32,14) (10,14) (25,10) (5,20) (27,12) (8,32) (22,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1233",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,17) (21,9) (6,5) (8,23) (2,26) (0,3) (6,21) (4,20) (20,1) (13,18) (4,19) (22,6) (11,23) (0,17) (3,9) (24,21) (3,10) (15,12) (0,1) (14,27) (15,22) (16,8) (1,13) (23,7) (0,2) (7,26) (20,12) (23,27) (25,24) (0,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph425",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (12,11) (9,27) (0,3) (18,27) (6,28) (1,6) (14,20) (21,12) (14,25) (24,15) (16,6) (19,13) (24,29) (13,9) (20,10) (23,28) (22,25) (23,7) (1,17) (8,14) (5,6) (0,15) (4,6) (2,18) (26,8) (9,11) (15,6) (3,18) (19,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1170",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,2) (6,14) (5,22) (23,12) (9,21) (11,0) (17,20) (16,0) (12,7) (8,4) (15,18) (1,6) (19,8) (5,26) (3,26) (0,1) (10,12) (11,20) (2,21) (9,25) (0,24) (7,6) (21,8) (23,22) (0,13) (18,25) (0,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1625",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (14,24) (26,8) (1,28) (0,1) (28,15) (4,8) (22,27) (24,11) (21,3) (28,14) (17,18) (2,0) (29,2) (28,9) (13,19) (20,0) (5,24) (1,7) (4,13) (30,6) (21,11) (25,19) (16,0) (22,20) (30,15) (31,18) (23,14) (29,21) (9,10) (1,27) (12,10) (22,18) (19,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1775",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (15,17) (29,21) (1,32) (0,1) (13,22) (7,5) (6,19) (32,25) (10,20) (11,18) (14,28) (23,28) (4,20) (8,14) (7,28) (29,0) (13,11) (27,16) (20,17) (12,0) (16,17) (3,7) (3,0) (9,28) (4,0) (8,2) (27,0) (2,0) (19,7) (17,22) (10,24) (9,26) (32,30) (15,26) (12,32) (31,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph154",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,19) (26,20) (17,9) (4,14) (25,2) (13,16) (0,25) (1,24) (9,26) (25,18) (1,6) (4,17) (16,17) (15,18) (20,10) (21,0) (4,0) (11,18) (2,3) (7,12) (7,20) (18,8) (10,23) (12,5) (1,26) (2,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph841",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,17) (15,24) (6,1) (20,6) (7,26) (4,25) (23,22) (10,15) (0,33) (23,18) (3,29) (16,17) (9,28) (13,17) (27,14) (20,5) (31,0) (10,8) (26,24) (25,1) (5,16) (12,23) (10,14) (22,11) (24,3) (9,32) (23,14) (11,13) (23,21) (33,30) (19,25) (8,28) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1365",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,16) (17,11) (8,6) (5,20) (16,5) (20,13) (2,6) (19,10) (27,22) (7,26) (23,1) (15,18) (1,12) (0,1) (6,25) (0,23) (9,13) (15,1) (21,19) (7,23) (24,17) (4,24) (28,25) (13,23) (3,21) (27,6) (13,22) (4,14) (21,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph237",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,22) (7,27) (8,25) (5,16) (17,0) (13,23) (0,1) (8,11) (15,1) (5,7) (7,11) (4,27) (3,10) (0,6) (10,14) (16,9) (12,26) (11,21) (12,8) (7,23) (14,22) (1,25) (22,11) (19,4) (3,24) (6,2) (18,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1060",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,20) (12,5) (25,10) (13,22) (17,24) (8,12) (2,0) (17,9) (23,10) (2,10) (12,23) (24,4) (0,1) (21,0) (0,18) (15,9) (7,22) (4,14) (3,7) (19,18) (3,0) (0,14) (12,1) (6,5) (21,7) (4,23) (8,16) (11,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph747",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (11,2) (5,13) (2,9) (21,26) (13,27) (6,8) (30,2) (12,28) (4,29) (22,18) (18,17) (31,0) (3,23) (12,1) (20,16) (4,28) (25,14) (6,25) (3,6) (11,19) (23,24) (8,19) (22,15) (16,28) (12,10) (18,19) (7,12) (18,31) (11,32) (26,0) (30,13) (28,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph327",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,5) (26,2) (23,6) (17,27) (1,8) (17,2) (7,24) (12,27) (4,28) (0,13) (8,21) (7,20) (9,3) (13,4) (15,5) (23,20) (9,23) (27,22) (25,11) (16,20) (19,21) (4,21) (27,6) (7,18) (21,10) (5,4) (0,9) (14,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1791",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,11) (11,27) (12,17) (3,0) (1,0) (3,7) (25,10) (29,19) (25,15) (10,2) (32,14) (27,16) (10,9) (0,28) (18,24) (5,29) (7,11) (28,26) (4,1) (25,31) (19,15) (0,30) (21,17) (4,26) (23,0) (17,13) (20,31) (2,0) (14,28) (9,23) (2,13) (18,2) (6,7) (8,26) (31,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1327",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,15) (26,4) (6,0) (3,1) (7,13) (5,12) (4,24) (5,26) (17,9) (13,21) (0,13) (22,11) (16,7) (0,3) (2,7) (6,27) (12,25) (23,3) (20,18) (19,10) (2,28) (4,8) (19,4) (23,6) (6,22) (24,14) (20,14) (0,1) (2,0) (17,4) (19,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph824",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,2) (1,15) (29,2) (32,1) (17,25) (15,8) (17,22) (20,22) (13,26) (2,32) (7,20) (22,5) (4,0) (25,3) (14,31) (26,10) (12,32) (27,24) (8,6) (4,16) (18,14) (33,16) (26,3) (29,9) (19,3) (9,30) (7,11) (28,17) (20,24) (27,6) (4,13) (25,23) (18,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1927",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,1) (34,11) (16,22) (20,23) (18,21) (0,4) (1,32) (18,33) (25,18) (0,1) (6,13) (10,26) (28,20) (31,21) (8,9) (24,21) (11,23) (31,2) (7,20) (0,32) (11,3) (31,15) (11,5) (19,4) (0,3) (21,28) (21,10) (8,25) (25,4) (1,27) (12,18) (2,0) (5,30) (22,17) (13,20) (22,29) (0,29) (27,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1271",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,13) (2,10) (18,11) (0,10) (1,26) (13,23) (1,6) (27,18) (16,20) (7,25) (19,1) (22,13) (5,4) (2,24) (13,1) (12,26) (16,6) (17,2) (17,14) (1,0) (7,2) (18,26) (20,8) (4,12) (11,3) (2,21) (9,1) (15,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph304",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,15) (25,16) (3,17) (13,16) (1,8) (6,20) (18,24) (8,14) (2,23) (22,5) (26,9) (10,7) (23,12) (4,14) (14,23) (17,27) (3,2) (21,1) (7,9) (19,5) (21,20) (13,11) (4,0) (28,26) (10,6) (22,12) (3,25) (11,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1385",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,26) (8,5) (22,17) (23,6) (22,25) (10,7) (25,2) (3,19) (22,24) (12,27) (11,16) (4,19) (11,5) (21,19) (23,22) (22,13) (0,2) (0,1) (25,7) (19,15) (4,12) (4,0) (2,1) (28,7) (14,17) (11,9) (21,18) (20,4) (0,20) (0,22) (9,23) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1965",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,25) (28,20) (2,0) (15,24) (27,5) (32,21) (13,26) (19,18) (0,3) (29,33) (15,16) (4,0) (34,21) (14,19) (21,14) (23,2) (23,14) (17,18) (30,34) (25,9) (24,8) (6,9) (0,26) (5,21) (34,15) (24,26) (3,12) (15,6) (19,11) (1,29) (1,4) (31,3) (28,19) (22,31) (10,12) (1,0) (7,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph783",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,6) (17,0) (14,32) (10,13) (19,25) (4,15) (2,11) (3,4) (29,23) (13,5) (30,24) (29,0) (10,16) (28,20) (31,10) (21,19) (16,18) (10,11) (20,5) (0,32) (1,7) (1,25) (9,22) (30,21) (30,26) (1,27) (7,22) (8,19) (23,21) (11,15) (12,10) (28,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1299",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,13) (11,12) (15,8) (26,14) (1,0) (17,10) (12,6) (21,18) (17,4) (6,1) (9,15) (25,17) (3,0) (16,10) (22,12) (0,4) (14,3) (0,2) (20,10) (6,23) (23,18) (14,7) (19,2) (15,1) (17,2) (24,23) (5,9) (15,25) (0,5) (16,27) (19,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph717",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,20) (12,14) (18,13) (7,6) (22,17) (15,1) (13,4) (31,2) (32,9) (23,30) (27,2) (9,26) (21,18) (10,16) (28,25) (23,4) (10,20) (8,1) (7,3) (11,21) (3,16) (14,10) (18,27) (24,0) (9,6) (24,19) (0,15) (17,24) (28,9) (5,24) (7,1) (8,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph925",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,32) (13,18) (7,13) (6,7) (23,29) (13,0) (2,24) (3,11) (31,16) (27,6) (27,34) (28,15) (9,26) (23,24) (7,1) (8,29) (17,21) (19,20) (33,30) (9,2) (5,30) (19,12) (34,8) (14,22) (3,4) (28,6) (25,34) (4,22) (17,23) (19,16) (10,5) (4,1) (11,31) (32,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph681",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (22,29) (24,11) (28,14) (4,29) (5,23) (1,29) (10,28) (22,9) (3,16) (3,26) (0,31) (15,2) (5,6) (11,20) (1,2) (13,17) (19,12) (27,14) (30,12) (5,3) (24,22) (25,9) (19,21) (30,1) (13,12) (26,19) (24,8) (11,18) (8,7) (10,2) (20,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph646",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (14,1) (13,18) (15,27) (14,19) (10,0) (11,6) (20,7) (12,4) (18,11) (7,23) (31,19) (4,23) (22,3) (30,9) (20,8) (28,10) (30,5) (18,30) (13,4) (26,16) (17,2) (3,29) (15,17) (20,15) (25,17) (21,19) (27,24) (28,7) (17,31) (20,3) (20,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph639",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,28) (17,14) (4,18) (29,9) (21,2) (3,18) (26,7) (18,1) (19,16) (13,21) (25,28) (23,27) (29,14) (6,28) (14,25) (8,10) (2,16) (8,7) (30,12) (28,30) (30,31) (23,14) (24,10) (12,20) (23,22) (27,15) (29,4) (5,14) (0,26) (16,7) (8,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1776",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,24) (17,28) (3,22) (0,2) (19,10) (5,7) (1,0) (11,30) (6,5) (28,27) (13,11) (23,31) (27,15) (13,3) (31,5) (0,14) (21,1) (27,22) (23,13) (8,12) (29,14) (4,18) (22,18) (20,0) (32,1) (2,23) (19,8) (25,26) (1,26) (24,6) (29,2) (32,23) (1,9) (12,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph203",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,4) (22,17) (25,22) (12,7) (14,17) (12,4) (16,11) (21,18) (4,19) (15,19) (22,24) (6,23) (10,7) (22,23) (11,5) (9,11) (19,3) (13,22) (10,26) (23,9) (25,2) (0,20) (25,27) (8,5) (22,0) (1,2) (21,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph654",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (18,11) (6,3) (2,11) (10,12) (12,7) (13,30) (15,22) (24,23) (3,23) (16,20) (0,31) (12,1) (21,26) (28,4) (6,8) (28,16) (13,27) (31,19) (17,18) (29,4) (28,24) (25,14) (13,5) (8,19) (22,18) (0,26) (2,30) (2,9) (19,18) (25,6) (12,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1773",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,12) (9,2) (28,26) (13,0) (4,25) (4,29) (4,0) (2,19) (21,32) (4,32) (32,18) (27,6) (4,30) (7,17) (10,29) (22,26) (2,0) (16,13) (31,25) (24,1) (30,8) (7,12) (6,24) (6,22) (3,0) (15,27) (0,5) (30,23) (16,6) (1,0) (14,2) (20,19) (12,22) (11,20) (11,22) (19,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1748",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,7) (0,26) (5,13) (19,8) (28,4) (32,11) (2,30) (0,31) (13,30) (12,1) (18,17) (29,4) (25,14) (12,28) (15,22) (2,11) (27,13) (18,19) (31,18) (24,23) (16,28) (25,6) (8,6) (21,26) (28,24) (3,23) (10,12) (1,0) (11,19) (9,2) (0,2) (20,16) (3,6) (18,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph755",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (11,8) (14,31) (5,9) (16,22) (18,3) (11,19) (18,13) (8,29) (25,0) (9,17) (28,27) (16,2) (17,0) (1,27) (7,32) (27,30) (4,21) (7,20) (23,27) (14,22) (16,5) (27,20) (26,28) (14,10) (23,31) (1,18) (4,13) (12,9) (14,15) (8,16) (11,6) (8,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph260",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,21) (15,18) (9,15) (5,25) (24,21) (25,24) (19,5) (3,1) (14,8) (8,22) (6,8) (9,14) (3,10) (27,26) (0,5) (22,3) (15,20) (7,12) (10,11) (5,27) (23,6) (20,17) (16,10) (6,7) (13,15) (21,2) (14,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1026",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,6) (23,8) (7,23) (1,6) (25,14) (21,12) (19,24) (1,0) (18,2) (4,6) (5,0) (16,6) (22,25) (14,20) (6,25) (13,9) (10,20) (15,6) (8,14) (11,12) (0,3) (13,19) (18,9) (0,2) (3,18) (0,15) (1,17) (11,9) (4,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph404",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,20) (2,29) (11,19) (24,4) (0,23) (1,15) (6,3) (17,12) (14,1) (10,13) (22,13) (23,7) (18,24) (21,26) (13,23) (19,16) (5,16) (6,27) (28,7) (19,21) (4,17) (6,25) (23,1) (9,6) (24,15) (25,29) (8,21) (20,5) (27,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1349",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,17) (27,7) (10,2) (9,11) (22,6) (13,4) (12,1) (20,28) (17,9) (20,25) (0,2) (13,1) (20,19) (27,3) (14,8) (25,15) (9,5) (11,4) (23,5) (0,1) (15,0) (14,4) (24,2) (15,6) (18,1) (27,6) (21,6) (26,2) (1,26) (12,16) (3,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1712",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (4,0) (7,11) (0,3) (2,23) (19,22) (14,8) (15,1) (5,30) (19,5) (4,5) (0,31) (0,1) (16,31) (21,6) (0,5) (7,6) (27,20) (19,8) (2,12) (12,5) (11,25) (17,24) (13,1) (32,21) (6,5) (16,19) (10,24) (5,28) (18,31) (26,23) (19,20) (14,3) (29,2) (2,0) (29,9) (10,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1652",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,18) (23,24) (27,14) (4,29) (1,3) (2,10) (5,20) (4,15) (4,30) (16,20) (9,31) (27,7) (21,18) (0,2) (0,1) (1,2) (1,8) (23,9) (2,13) (28,21) (14,21) (30,22) (3,19) (25,30) (17,9) (25,6) (29,26) (29,7) (4,0) (25,5) (28,17) (14,11) (12,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1721",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,5) (23,29) (0,14) (29,21) (7,16) (5,31) (1,0) (1,17) (29,12) (30,24) (27,24) (13,25) (14,1) (2,0) (32,15) (32,6) (8,15) (12,25) (10,12) (31,14) (24,4) (26,17) (13,19) (28,31) (8,9) (20,1) (23,3) (26,30) (6,16) (2,5) (2,11) (18,8) (7,24) (22,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1703",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,19) (12,1) (1,28) (14,24) (10,16) (28,14) (26,8) (0,20) (27,1) (11,19) (2,32) (22,18) (14,23) (29,3) (19,25) (32,13) (1,0) (30,21) (24,6) (7,30) (11,21) (18,20) (32,22) (28,15) (9,28) (11,24) (17,0) (5,21) (15,31) (9,10) (4,13) (4,8) (22,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph650",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,24) (27,6) (3,26) (16,31) (20,24) (15,1) (20,7) (16,4) (2,14) (6,8) (13,26) (28,9) (8,15) (29,2) (26,10) (9,29) (22,17) (0,4) (18,14) (17,21) (7,11) (22,5) (23,18) (13,4) (20,22) (25,3) (3,12) (2,19) (17,25) (25,23) (1,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph663",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,1) (12,25) (9,18) (30,13) (18,4) (0,28) (17,15) (23,31) (14,27) (5,20) (3,19) (8,21) (27,23) (27,29) (2,31) (2,1) (21,15) (30,16) (4,5) (8,26) (6,2) (28,10) (3,14) (13,6) (11,16) (28,7) (22,24) (5,24) (18,12) (4,19) (14,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1490",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,4) (0,6) (11,29) (19,7) (3,0) (3,5) (15,1) (20,4) (20,3) (21,25) (29,6) (18,25) (6,14) (20,24) (22,26) (0,1) (2,0) (24,26) (29,17) (28,22) (10,17) (2,4) (6,25) (8,16) (23,24) (14,13) (2,27) (20,19) (21,12) (22,8) (0,15) (9,12) (27,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph432",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,16) (24,6) (28,17) (10,22) (15,3) (16,27) (11,17) (5,13) (0,17) (3,21) (4,25) (27,17) (16,24) (13,23) (20,7) (9,12) (6,7) (29,16) (1,10) (6,18) (22,24) (27,25) (19,22) (9,25) (8,17) (26,21) (15,20) (5,4) (4,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1376",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,19) (25,5) (26,25) (8,24) (10,11) (15,27) (13,6) (25,1) (26,6) (7,12) (9,15) (8,2) (7,4) (9,3) (0,1) (21,20) (3,14) (18,17) (0,16) (5,15) (17,4) (10,6) (26,0) (17,20) (28,26) (0,2) (21,16) (8,0) (27,23) (19,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1530",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (24,26) (2,0) (19,2) (7,9) (25,24) (7,11) (11,23) (19,4) (0,18) (21,9) (28,10) (1,0) (28,0) (10,8) (20,5) (1,16) (12,17) (26,19) (22,14) (29,23) (4,5) (30,2) (21,4) (27,0) (14,21) (14,6) (16,17) (26,3) (15,26) (12,15) (10,9) (13,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1807",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,0) (9,1) (0,22) (32,17) (8,26) (9,5) (12,30) (26,28) (24,27) (14,29) (13,16) (4,9) (0,23) (10,18) (4,25) (33,19) (20,15) (14,2) (3,10) (7,31) (11,18) (26,27) (31,21) (26,6) (15,0) (32,27) (14,30) (23,1) (2,21) (11,32) (0,2) (2,28) (23,7) (5,33) (13,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph641",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,22) (10,25) (1,11) (30,6) (27,26) (0,23) (19,25) (18,4) (12,8) (22,14) (29,27) (16,20) (29,4) (17,19) (31,0) (24,6) (4,17) (6,25) (3,16) (20,0) (2,13) (14,9) (16,13) (18,1) (11,15) (0,12) (24,5) (27,16) (28,22) (21,23) (1,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph946",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,11) (15,27) (10,12) (4,29) (16,13) (13,0) (20,19) (6,16) (4,25) (19,2) (7,17) (2,9) (0,3) (32,34) (22,26) (22,12) (11,22) (24,1) (30,26) (21,32) (31,4) (24,33) (14,2) (29,10) (6,27) (22,6) (23,30) (19,5) (18,32) (28,6) (8,30) (32,4) (25,33) (12,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1616",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,14) (9,27) (27,11) (5,20) (30,11) (24,9) (10,23) (27,13) (15,17) (14,15) (0,3) (19,1) (6,22) (24,8) (20,24) (25,21) (1,3) (18,24) (26,16) (18,12) (0,2) (25,17) (6,31) (16,8) (23,2) (30,7) (14,4) (8,29) (9,28) (10,1) (31,25) (0,1) (23,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph540",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,22) (0,19) (8,12) (22,24) (28,8) (8,11) (0,6) (25,11) (12,29) (27,4) (5,17) (22,14) (25,20) (3,10) (6,9) (7,11) (23,15) (29,5) (3,27) (0,1) (1,28) (23,21) (10,14) (4,21) (30,7) (30,2) (16,13) (7,18) (1,16) (26,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph714",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,11) (18,32) (16,6) (4,25) (14,2) (7,17) (25,31) (29,4) (32,21) (24,6) (11,20) (26,22) (2,9) (22,12) (22,6) (27,6) (12,10) (19,2) (12,7) (20,19) (30,23) (0,3) (29,10) (1,24) (8,30) (16,13) (0,13) (19,5) (32,4) (4,30) (26,28) (15,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1257",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,2) (0,2) (5,24) (1,0) (0,3) (13,10) (7,1) (9,0) (4,19) (11,19) (21,17) (18,6) (8,22) (24,22) (0,16) (17,4) (17,24) (12,21) (11,23) (4,0) (6,14) (27,15) (3,9) (26,23) (14,16) (27,14) (15,1) (16,8) (25,24) (10,26) (15,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1051",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,2) (14,18) (4,11) (17,5) (22,6) (0,15) (20,12) (7,6) (20,13) (0,2) (7,21) (19,2) (15,22) (3,0) (12,15) (25,20) (17,23) (19,8) (7,1) (4,9) (18,0) (15,11) (8,17) (4,0) (19,10) (17,24) (0,1) (18,3) (17,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph879",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,21) (20,12) (6,7) (14,1) (13,31) (23,24) (32,10) (11,9) (5,17) (29,25) (33,2) (8,1) (24,17) (23,6) (6,12) (31,21) (0,5) (12,15) (16,32) (19,30) (27,9) (11,28) (8,0) (17,26) (32,3) (23,22) (11,25) (4,8) (30,23) (19,33) (2,18) (10,7) (25,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1157",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,11) (11,15) (6,1) (18,1) (23,5) (8,3) (12,14) (13,26) (22,13) (14,11) (1,25) (23,8) (0,3) (9,16) (24,20) (2,7) (16,13) (20,0) (17,1) (19,4) (0,14) (2,0) (7,0) (10,15) (4,5) (25,21) (26,2) (12,17) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph451",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,24) (5,4) (16,1) (15,26) (17,8) (7,9) (14,21) (23,11) (18,5) (11,7) (17,0) (16,12) (10,6) (9,10) (0,28) (3,14) (20,14) (28,23) (24,22) (13,17) (26,2) (15,12) (4,21) (21,9) (10,27) (19,25) (19,4) (0,26) (19,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1845",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,32) (27,7) (23,20) (9,6) (11,24) (17,32) (9,5) (29,31) (7,24) (8,24) (32,31) (3,33) (32,10) (0,1) (8,30) (4,24) (9,28) (18,2) (0,3) (23,13) (21,27) (17,11) (29,15) (6,14) (3,4) (6,26) (0,2) (12,29) (6,10) (22,25) (16,31) (19,27) (4,0) (23,11) (1,18) (3,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1402",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,15) (7,1) (25,2) (26,18) (22,24) (26,6) (3,11) (26,5) (9,23) (1,20) (8,11) (17,2) (20,25) (11,27) (0,11) (21,17) (21,19) (29,24) (0,1) (13,1) (10,13) (15,29) (28,24) (9,16) (1,12) (6,12) (22,25) (18,4) (24,0) (23,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1935",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (34,17) (0,2) (13,33) (0,5) (31,20) (27,16) (32,7) (25,15) (17,21) (3,6) (32,0) (33,18) (11,31) (25,22) (0,3) (20,10) (5,8) (34,10) (32,13) (24,27) (19,23) (3,1) (24,22) (2,21) (15,28) (11,18) (4,23) (9,11) (18,1) (4,26) (30,31) (31,26) (29,7) (15,12) (17,14) (1,0) (25,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1435",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,23) (13,17) (8,15) (27,24) (20,10) (4,5) (7,26) (7,5) (12,8) (7,0) (26,17) (14,27) (26,1) (29,12) (21,18) (17,3) (1,0) (3,0) (29,19) (22,17) (0,2) (25,12) (7,9) (16,2) (16,20) (6,26) (10,18) (11,21) (23,22) (16,17) (28,8) (11,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1833",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,23) (27,0) (7,17) (1,12) (18,19) (24,1) (0,1) (25,0) (26,2) (5,19) (31,29) (7,6) (13,2) (33,27) (16,10) (17,30) (23,4) (8,16) (27,1) (13,22) (19,30) (31,14) (19,9) (15,23) (21,17) (11,3) (4,17) (11,27) (28,22) (32,22) (5,8) (26,29) (20,27) (29,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1772",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (2,6) (23,11) (6,28) (30,9) (3,5) (0,1) (12,30) (26,23) (6,20) (1,17) (26,19) (9,0) (13,20) (16,26) (12,32) (12,2) (8,2) (12,22) (6,18) (31,4) (21,5) (5,25) (2,0) (31,18) (27,29) (31,15) (14,1) (16,7) (0,10) (21,27) (12,17) (16,28) (5,23) (24,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1684",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,0) (19,17) (21,10) (31,28) (0,2) (5,14) (9,0) (1,0) (8,9) (29,17) (28,27) (30,2) (26,13) (14,3) (11,24) (25,5) (12,4) (30,18) (0,3) (3,13) (0,4) (14,20) (4,21) (25,21) (24,23) (1,3) (10,23) (30,1) (23,16) (0,22) (28,9) (12,29) (27,5) (17,6) (22,7)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1403",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,4) (3,17) (20,1) (11,15) (10,22) (13,26) (0,16) (27,7) (0,3) (28,1) (14,23) (23,18) (15,27) (7,24) (5,3) (7,12) (19,2) (20,25) (0,1) (24,14) (25,9) (29,3) (0,26) (0,2) (6,23) (16,22) (29,21) (0,4) (17,12) (28,11) (5,26) (11,8) (20,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph277",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,3) (7,16) (9,16) (27,0) (8,25) (18,4) (9,0) (11,16) (4,19) (26,8) (13,23) (9,10) (10,13) (12,11) (8,22) (3,24) (2,21) (3,21) (5,1) (24,10) (8,19) (20,18) (12,6) (15,16) (25,1) (14,3) (17,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1064",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,0) (11,2) (0,3) (2,12) (1,0) (2,0) (0,19) (21,15) (5,24) (9,13) (10,14) (23,11) (16,0) (22,18) (12,14) (4,0) (20,10) (9,10) (25,17) (7,6) (22,25) (15,11) (4,17) (5,3) (22,16) (15,1) (10,5) (10,8) (6,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1236",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (19,16) (3,24) (27,21) (0,1) (6,4) (24,16) (8,26) (3,0) (8,13) (17,1) (2,10) (18,24) (23,1) (11,20) (25,11) (27,10) (24,5) (4,9) (7,23) (13,9) (23,25) (10,12) (15,18) (17,0) (3,27) (22,18) (14,4) (25,22) (2,0) (20,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph436",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,24) (13,11) (24,11) (26,29) (3,2) (22,5) (27,17) (4,0) (14,23) (8,1) (9,26) (13,16) (3,25) (8,14) (21,1) (12,22) (17,3) (16,25) (9,7) (23,2) (20,6) (10,6) (7,10) (14,15) (23,12) (5,19) (21,29) (4,14) (28,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1209",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,13) (24,17) (1,23) (24,21) (24,4) (0,1) (21,3) (15,18) (14,4) (11,17) (13,22) (21,19) (6,26) (20,13) (7,23) (6,8) (2,6) (23,0) (15,1) (25,7) (1,12) (6,27) (27,22) (19,10) (13,9) (16,19) (20,5) (5,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph745",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,9) (2,1) (11,10) (0,3) (13,10) (5,3) (23,5) (17,26) (27,10) (2,17) (20,29) (21,23) (32,20) (27,24) (22,28) (15,14) (16,8) (20,11) (30,24) (6,10) (7,19) (16,27) (14,1) (28,23) (1,11) (32,25) (19,32) (25,18) (15,31) (2,12) (29,23) (4,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1654",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,9) (4,8) (28,14) (24,5) (6,30) (24,11) (2,29) (0,16) (18,17) (15,30) (20,22) (1,27) (0,1) (18,22) (23,14) (7,1) (12,10) (21,3) (20,0) (26,8) (22,27) (11,21) (28,1) (15,28) (13,19) (4,13) (29,21) (31,18) (25,19) (28,9) (11,19) (24,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph396",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,21) (17,20) (9,21) (23,12) (8,19) (26,27) (11,2) (7,12) (28,3) (1,6) (0,16) (0,24) (0,3) (13,0) (27,2) (4,8) (15,18) (25,18) (9,25) (10,12) (11,20) (6,14) (21,28) (7,6) (26,5) (0,11) (22,5) (22,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1188",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,20) (22,26) (23,18) (1,0) (16,24) (3,26) (10,23) (26,14) (4,24) (17,16) (10,8) (3,16) (2,22) (0,11) (20,19) (12,3) (23,12) (2,15) (14,13) (1,25) (26,7) (17,6) (0,5) (25,13) (26,9) (24,0) (21,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1311",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (15,19) (8,1) (0,7) (19,9) (26,19) (24,16) (5,2) (26,5) (20,12) (0,1) (0,3) (23,14) (17,20) (16,28) (18,26) (2,4) (1,12) (13,0) (2,0) (22,12) (6,21) (14,0) (25,7) (9,11) (8,6) (27,26) (3,17) (20,4) (19,16) (25,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph723",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,31) (16,12) (4,14) (17,32) (27,11) (29,10) (22,29) (32,6) (19,13) (27,31) (1,26) (28,27) (15,25) (5,29) (1,25) (5,12) (18,22) (21,7) (8,30) (1,7) (17,0) (19,12) (9,11) (2,7) (20,28) (4,31) (32,18) (22,26) (23,16) (11,3) (16,3) (26,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1424",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (25,29) (14,12) (16,21) (0,2) (13,27) (15,3) (13,6) (0,14) (7,8) (3,0) (4,23) (25,0) (8,18) (0,1) (9,5) (10,21) (21,4) (19,23) (9,19) (9,27) (28,26) (22,20) (7,0) (13,15) (24,9) (17,22) (20,7) (11,1) (0,9) (10,26) (7,11) (2,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1557",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,18) (29,5) (0,4) (24,18) (16,15) (27,16) (26,25) (0,1) (3,0) (2,17) (17,7) (5,6) (28,22) (14,3) (25,19) (8,27) (16,21) (23,27) (27,1) (9,14) (13,14) (28,25) (29,10) (20,19) (24,11) (3,5) (14,0) (17,25) (9,4) (22,30) (15,20) (2,4) (12,14) (0,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph355",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,15) (16,0) (15,5) (12,7) (19,7) (0,8) (26,25) (26,0) (6,26) (8,24) (20,17) (22,19) (23,27) (17,4) (1,25) (18,17) (9,3) (16,21) (21,20) (26,28) (9,15) (11,10) (7,4) (8,2) (10,6) (6,13) (3,14) (5,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph6",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,0) (12,9) (14,6) (20,3) (21,6) (4,2) (17,10) (12,0) (25,6) (13,14) (24,20) (7,19) (24,19) (22,23) (25,16) (21,11) (8,22) (15,1) (18,25) (5,3) (17,20) (24,22) (8,15) (20,4) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph524",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (30,4) (27,26) (2,15) (12,20) (26,11) (25,23) (0,30) (1,18) (9,28) (5,21) (25,22) (17,23) (27,23) (19,8) (29,6) (20,13) (14,2) (13,5) (30,27) (27,7) (27,3) (1,10) (5,16) (19,6) (21,24) (11,2) (21,18) (1,19) (8,9) (25,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1862",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (25,4) (29,8) (22,30) (31,17) (27,31) (7,28) (21,32) (24,19) (29,9) (0,3) (1,11) (28,5) (18,13) (0,1) (5,26) (12,23) (21,11) (23,13) (29,5) (10,16) (20,13) (23,24) (11,27) (12,15) (10,3) (16,2) (24,25) (29,6) (24,22) (2,0) (19,28) (24,11) (14,15) (16,13) (33,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1635",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (31,30) (12,22) (19,27) (22,16) (2,6) (14,10) (27,25) (1,2) (0,3) (23,28) (0,1) (5,18) (19,17) (3,22) (6,28) (17,14) (7,5) (4,0) (26,30) (20,21) (26,28) (1,13) (5,31) (26,21) (18,4) (26,11) (14,26) (12,27) (0,5) (22,8) (2,0) (9,25) (12,29) (10,24) (14,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph360",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,1) (3,21) (16,7) (5,28) (12,6) (24,10) (4,19) (3,24) (4,18) (9,16) (23,13) (12,11) (25,1) (27,9) (25,8) (8,26) (0,21) (11,16) (8,22) (10,28) (19,8) (3,14) (26,3) (17,6) (16,15) (20,18) (28,9) (10,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph608",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,2) (21,0) (12,6) (16,4) (1,14) (13,27) (0,30) (17,23) (17,14) (1,20) (24,18) (24,10) (27,19) (28,14) (6,25) (3,4) (6,20) (31,15) (7,31) (24,13) (29,1) (9,30) (7,5) (16,1) (28,22) (28,31) (1,26) (11,13) (24,0) (1,27) (8,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph825",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (33,12) (24,19) (32,16) (33,0) (5,9) (25,26) (6,28) (30,22) (28,20) (2,3) (32,21) (2,5) (23,11) (7,28) (18,11) (1,15) (20,29) (12,17) (3,4) (29,8) (11,6) (2,12) (1,29) (14,33) (14,32) (28,25) (12,28) (4,30) (31,15) (19,9) (27,10) (0,10) (13,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1335",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,22) (14,12) (5,25) (3,5) (2,11) (9,10) (1,0) (24,12) (0,19) (14,10) (20,28) (28,0) (15,1) (8,10) (6,7) (22,16) (9,13) (10,20) (22,18) (11,23) (17,25) (0,26) (6,25) (10,5) (2,20) (17,4) (15,21) (27,16) (15,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1150",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,11) (4,0) (25,15) (9,13) (2,26) (3,0) (10,24) (18,1) (22,8) (18,5) (6,2) (15,23) (21,9) (4,5) (1,0) (7,12) (0,24) (14,11) (16,15) (20,5) (26,10) (0,21) (7,14) (0,2) (5,19) (16,0) (8,20) (17,16) (3,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1428",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,1) (14,3) (14,0) (29,5) (27,29) (2,0) (28,27) (2,16) (8,15) (21,18) (26,2) (4,9) (22,6) (21,7) (27,21) (13,21) (9,6) (1,0) (29,10) (26,9) (15,12) (20,9) (26,23) (19,1) (11,8) (20,25) (0,3) (23,19) (14,2) (17,2) (2,24) (12,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1740",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,3) (22,24) (14,31) (0,3) (23,8) (2,1) (11,31) (22,30) (9,31) (2,25) (1,0) (16,29) (2,0) (10,2) (13,10) (15,28) (20,17) (0,6) (26,24) (4,15) (18,16) (7,29) (0,13) (30,5) (11,19) (26,18) (29,15) (29,8) (21,23) (27,8) (17,12) (28,32) (23,19) (2,26) (4,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph40",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,25) (15,11) (6,4) (10,1) (18,3) (2,6) (19,0) (5,2) (16,22) (7,9) (24,17) (7,15) (4,9) (17,0) (11,19) (13,23) (0,12) (22,15) (25,23) (20,16) (14,1) (16,1) (10,21) (3,10) (8,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1422",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,29) (28,8) (24,17) (6,4) (0,4) (5,13) (7,11) (0,5) (18,19) (29,9) (15,14) (15,21) (3,21) (3,0) (10,26) (26,23) (23,27) (8,11) (25,28) (3,26) (26,12) (0,18) (1,24) (0,2) (6,25) (1,0) (20,14) (13,25) (2,20) (17,22) (1,16) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1176",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,12) (20,10) (9,6) (5,9) (3,0) (16,25) (0,7) (20,26) (3,22) (2,0) (10,25) (16,8) (17,21) (13,2) (5,24) (13,8) (22,18) (13,23) (11,14) (25,4) (17,19) (15,22) (11,9) (24,23) (4,0) (0,1) (12,26) (16,1) (8,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph410",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,10) (25,11) (19,10) (13,29) (29,6) (2,7) (9,4) (5,29) (4,7) (5,14) (28,20) (22,16) (8,1) (17,27) (28,25) (12,0) (17,21) (3,23) (13,28) (23,29) (19,0) (3,18) (2,26) (23,21) (8,7) (24,11) (14,15) (22,20) (19,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1239",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,10) (8,25) (0,4) (25,19) (4,9) (24,3) (16,4) (6,18) (20,12) (21,26) (13,16) (17,8) (27,17) (8,1) (0,3) (24,5) (0,27) (1,0) (6,16) (13,7) (11,18) (12,25) (0,2) (22,9) (3,19) (15,23) (4,24) (26,9) (14,15) (12,2) (15,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph695",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,29) (19,3) (29,25) (24,8) (17,11) (30,19) (23,4) (21,4) (20,13) (18,14) (31,19) (22,10) (31,6) (18,8) (24,7) (20,30) (10,26) (15,16) (8,23) (9,15) (7,27) (27,5) (1,0) (6,16) (13,29) (28,29) (12,28) (1,26) (2,4) (13,0) (23,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1201",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,20) (18,24) (0,1) (2,19) (1,27) (20,10) (12,0) (4,0) (14,15) (18,6) (3,7) (0,26) (5,17) (17,23) (9,16) (11,19) (25,6) (8,20) (0,3) (0,24) (2,0) (6,1) (8,18) (24,9) (2,10) (13,17) (27,4) (7,22) (22,13) (11,3) (21,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1932",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,19) (25,7) (14,20) (20,22) (15,6) (33,23) (0,2) (17,5) (17,32) (16,29) (27,25) (0,4) (7,4) (33,10) (21,7) (21,1) (5,1) (4,15) (16,11) (31,9) (29,19) (10,0) (28,25) (8,17) (24,34) (2,6) (10,9) (16,23) (18,28) (3,33) (13,17) (1,0) (22,16) (14,30) (12,18) (24,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph823",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,12) (30,11) (29,18) (9,25) (29,15) (5,11) (8,20) (6,4) (27,1) (17,32) (31,33) (0,12) (24,12) (22,13) (11,32) (26,20) (13,9) (33,0) (4,15) (28,8) (8,10) (8,16) (12,8) (28,14) (26,19) (3,8) (7,14) (2,7) (1,26) (6,26) (14,17) (10,23) (21,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph885",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,16) (13,11) (22,28) (12,6) (5,7) (24,18) (6,25) (1,29) (33,1) (28,8) (23,17) (13,24) (6,20) (27,13) (3,4) (1,26) (24,10) (28,31) (20,1) (32,14) (30,9) (14,28) (30,0) (21,0) (7,31) (0,24) (27,19) (31,33) (17,14) (8,2) (27,1) (16,4) (31,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph620",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,17) (1,11) (6,27) (17,22) (20,13) (29,10) (12,23) (10,19) (21,6) (1,24) (9,5) (27,4) (22,0) (21,25) (24,18) (30,13) (15,19) (3,24) (28,23) (9,0) (31,13) (8,14) (3,5) (2,22) (23,16) (3,16) (14,4) (19,18) (26,9) (7,1) (24,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph218",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,0) (11,7) (4,19) (22,11) (6,2) (10,3) (13,23) (8,12) (25,8) (7,23) (15,1) (11,8) (0,17) (24,3) (7,5) (21,11) (27,4) (1,25) (21,18) (14,22) (5,16) (16,9) (10,14) (26,12) (22,20) (0,1) (7,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1953",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,27) (5,11) (20,7) (8,25) (15,31) (10,26) (23,11) (25,4) (5,30) (8,9) (21,28) (0,1) (34,11) (29,22) (31,2) (20,28) (14,1) (13,6) (20,23) (4,19) (11,3) (32,1) (32,0) (27,1) (2,0) (21,18) (22,16) (33,18) (21,10) (0,29) (12,18) (22,17) (24,21) (21,31) (18,25) (20,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph17",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,15) (7,6) (5,15) (23,25) (7,12) (10,16) (22,8) (11,10) (20,17) (22,3) (20,6) (9,15) (21,2) (16,21) (8,14) (24,25) (4,14) (1,3) (5,0) (8,6) (14,9) (21,24) (15,13) (5,19) (3,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1194",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (24,26) (1,0) (0,2) (2,17) (7,6) (5,11) (2,6) (10,7) (11,3) (19,10) (10,11) (8,20) (22,21) (15,0) (9,7) (17,21) (12,22) (20,7) (10,15) (11,4) (2,26) (8,1) (17,18) (24,14) (16,2) (15,13) (3,25) (4,23)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1553",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,0) (24,4) (14,2) (9,19) (19,23) (8,23) (18,6) (15,6) (13,23) (22,17) (21,16) (15,27) (12,16) (2,0) (24,12) (13,29) (5,10) (19,18) (1,12) (3,6) (17,2) (25,6) (2,30) (8,20) (28,25) (26,19) (3,0) (7,4) (0,1) (28,30) (7,5) (11,7) (4,0) (22,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph454",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,6) (0,17) (27,24) (15,22) (20,12) (10,21) (21,24) (5,6) (23,4) (12,15) (1,19) (27,14) (6,29) (28,22) (12,17) (28,4) (11,23) (25,20) (26,0) (9,29) (7,3) (3,9) (1,20) (13,18) (2,26) (16,8) (8,23) (29,26) (28,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1439",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,27) (11,24) (16,23) (10,29) (21,19) (11,6) (19,17) (20,14) (5,2) (17,4) (26,12) (20,7) (17,29) (16,29) (14,27) (1,0) (8,19) (0,4) (27,3) (11,2) (9,22) (9,2) (12,13) (7,25) (19,28) (3,0) (10,15) (0,2) (2,15) (11,25) (0,13) (3,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1782",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,15) (0,2) (25,27) (19,29) (9,23) (13,17) (9,10) (25,26) (4,0) (5,1) (10,31) (24,13) (0,1) (11,18) (17,30) (4,12) (16,23) (16,8) (7,21) (20,14) (16,22) (17,5) (15,3) (22,20) (10,0) (19,18) (28,16) (14,29) (7,4) (6,17) (2,6) (32,24) (25,7) (21,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph242",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (8,19) (26,2) (27,21) (25,18) (22,23) (5,22) (7,6) (15,18) (12,23) (9,21) (12,10) (3,27) (17,20) (13,0) (25,9) (4,8) (11,0) (21,8) (5,26) (6,14) (11,20) (1,6) (11,2) (7,12) (3,0) (0,16) (0,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph164",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,9) (25,15) (26,18) (15,8) (6,15) (17,2) (3,22) (26,21) (19,11) (20,25) (23,17) (21,7) (18,12) (0,6) (8,11) (5,2) (16,20) (11,2) (9,24) (14,22) (18,14) (4,1) (9,8) (21,1) (23,4) (10,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1524",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,11) (0,12) (0,27) (24,14) (1,12) (6,2) (19,5) (9,5) (25,4) (3,27) (23,21) (16,24) (4,22) (6,10) (28,19) (4,13) (10,20) (21,13) (15,16) (18,0) (14,13) (17,22) (30,4) (21,10) (5,14) (0,1) (26,7) (30,7) (28,8) (3,22) (29,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1137",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,18) (16,4) (3,0) (5,13) (19,3) (15,11) (18,6) (0,12) (2,0) (2,24) (20,26) (24,3) (15,13) (19,25) (7,1) (16,6) (17,26) (1,8) (12,14) (8,25) (25,12) (9,21) (0,1) (17,8) (22,15) (10,16) (4,9) (23,9) (4,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1432",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,29) (14,3) (11,28) (0,13) (5,20) (17,13) (17,11) (9,18) (13,15) (2,18) (8,25) (8,1) (0,1) (3,0) (4,3) (10,15) (16,7) (26,24) (12,16) (27,0) (6,16) (13,8) (6,14) (21,9) (19,18) (12,22) (23,16) (27,24) (5,14) (2,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph65",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,9) (0,19) (2,10) (8,4) (9,6) (10,13) (7,0) (17,11) (25,4) (3,24) (24,6) (2,1) (7,4) (15,22) (14,19) (11,2) (16,8) (13,23) (5,18) (10,21) (18,2) (4,20) (22,21) (12,19) (14,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1191",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,1) (0,1) (21,3) (19,22) (10,4) (16,5) (19,4) (2,8) (25,20) (4,14) (14,11) (21,19) (0,21) (16,11) (12,13) (12,0) (11,26) (8,15) (7,25) (15,18) (20,8) (11,9) (24,22) (23,14) (6,21) (0,17) (7,17)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1567",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,13) (29,21) (18,0) (17,29) (16,28) (24,19) (10,26) (16,22) (21,30) (30,19) (21,27) (0,1) (26,6) (14,15) (2,20) (15,16) (7,8) (30,10) (12,28) (4,26) (3,7) (20,11) (1,5) (25,16) (30,9) (18,17) (5,23) (8,15) (5,20) (9,14) (20,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph754",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,25) (8,14) (14,28) (0,30) (17,8) (18,7) (10,25) (15,23) (26,24) (13,31) (5,27) (13,32) (22,9) (5,7) (15,13) (16,2) (9,2) (28,21) (7,6) (26,13) (13,12) (7,1) (21,30) (19,14) (11,9) (0,4) (3,8) (3,2) (20,8) (29,12) (25,21) (1,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph812",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,20) (33,13) (11,14) (22,17) (32,10) (28,9) (3,5) (15,4) (16,23) (30,5) (23,14) (12,1) (8,1) (21,6) (2,33) (4,27) (24,3) (32,27) (22,7) (0,22) (24,1) (33,9) (23,31) (26,21) (0,9) (6,29) (6,17) (16,3) (18,24) (20,13) (25,19) (19,10) (18,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1464",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,17) (8,25) (16,7) (3,14) (15,13) (0,13) (28,11) (6,14) (20,5) (2,18) (18,9) (16,12) (1,8) (11,17) (3,4) (26,24) (15,10) (1,0) (9,21) (8,13) (19,18) (5,14) (0,3) (29,15) (27,24) (6,16) (27,0) (16,23) (22,12) (2,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1552",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,8) (4,10) (18,25) (0,2) (19,20) (29,18) (28,1) (4,16) (28,26) (1,0) (10,24) (27,20) (3,4) (21,8) (6,23) (10,15) (0,13) (11,24) (2,3) (30,15) (7,21) (28,12) (21,28) (22,3) (5,0) (28,14) (28,13) (27,23) (5,27) (9,25) (30,18) (2,13)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1214",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,19) (24,13) (17,11) (8,4) (7,27) (0,1) (22,15) (9,22) (12,19) (4,27) (0,7) (21,10) (6,25) (2,18) (0,2) (21,22) (18,27) (16,8) (1,2) (5,14) (0,19) (2,20) (10,2) (23,4) (10,13) (5,26) (27,11) (3,24) (6,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1425",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,0) (18,23) (14,0) (3,10) (13,7) (17,24) (22,16) (5,2) (26,1) (11,15) (29,25) (16,23) (24,25) (16,1) (28,12) (29,2) (2,0) (6,4) (0,17) (1,20) (3,21) (15,28) (15,7) (10,26) (4,9) (0,1) (27,10) (8,6) (22,9) (0,19) (11,19) (28,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph297",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,9) (23,11) (9,2) (16,12) (26,7) (21,15) (14,23) (23,4) (27,19) (27,24) (23,13) (15,17) (10,12) (9,5) (6,1) (23,10) (8,2) (4,3) (18,5) (25,12) (26,16) (24,17) (0,2) (13,17) (12,22) (20,21) (11,2)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph353",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,16) (9,13) (21,14) (22,0) (5,20) (27,5) (5,19) (26,2) (23,8) (28,24) (6,2) (15,26) (10,7) (28,7) (11,17) (25,3) (12,14) (1,18) (21,5) (28,9) (27,15) (3,0) (4,5) (16,15) (0,16) (8,20) (5,11) (24,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1759",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,2) (19,11) (25,28) (15,4) (15,0) (29,14) (10,30) (26,7) (1,0) (31,26) (22,11) (14,17) (3,32) (27,0) (24,2) (17,1) (26,18) (20,28) (2,0) (24,23) (8,10) (17,31) (12,26) (5,3) (10,28) (23,9) (21,0) (6,30) (13,2) (2,22) (4,10) (32,24) (16,8) (30,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1753",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,12) (0,31) (24,23) (4,29) (3,6) (12,10) (1,0) (19,11) (9,2) (18,17) (25,14) (12,28) (21,26) (30,2) (18,31) (19,18) (26,0) (28,24) (2,0) (1,12) (15,22) (5,13) (3,23) (4,28) (11,2) (27,13) (8,19) (16,28) (6,25) (6,8) (22,18) (30,13) (11,32) (16,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph11",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,25) (12,18) (13,19) (24,23) (12,13) (24,11) (20,17) (15,0) (19,24) (15,10) (22,12) (2,8) (15,3) (7,24) (9,2) (4,18) (21,6) (0,24) (5,25) (8,3) (4,1) (14,15) (0,25) (14,16) (6,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1206",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (11,10) (11,4) (19,12) (16,12) (17,23) (8,10) (2,13) (26,27) (24,8) (14,16) (13,20) (5,2) (19,1) (14,7) (17,6) (15,25) (0,3) (26,0) (1,0) (15,23) (12,18) (21,0) (25,8) (17,0) (18,9) (1,25) (22,3) (13,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph52",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,21) (13,21) (15,2) (19,9) (15,3) (13,15) (20,7) (7,8) (10,21) (0,9) (17,8) (0,7) (14,0) (23,4) (25,9) (19,23) (11,1) (10,24) (20,18) (16,22) (7,11) (6,13) (12,14) (9,5) (22,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1717",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (3,0) (16,0) (23,32) (28,3) (16,19) (12,30) (2,7) (29,23) (32,21) (21,4) (15,5) (20,7) (25,12) (15,11) (0,2) (13,19) (17,30) (16,24) (12,15) (27,7) (29,18) (15,10) (9,31) (31,8) (6,12) (0,1) (31,12) (1,11) (28,10) (22,18) (11,14) (0,21) (16,26) (11,20) (13,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph561",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,17) (26,24) (11,3) (7,19) (8,12) (7,9) (10,2) (9,22) (30,21) (13,26) (25,17) (9,20) (23,24) (9,12) (7,15) (14,4) (11,6) (29,6) (13,18) (27,9) (21,0) (29,27) (16,1) (14,15) (28,2) (25,10) (30,5) (7,10) (1,0) (26,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1519",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (5,16) (9,13) (29,12) (23,25) (11,1) (0,4) (1,2) (11,19) (22,12) (19,27) (10,15) (1,0) (12,11) (16,7) (0,27) (0,24) (3,12) (6,19) (14,7) (0,8) (26,18) (9,15) (13,20) (26,5) (0,3) (21,28) (20,28) (20,3) (30,23) (23,28) (18,4) (10,17) (16,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph616",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,4) (15,6) (24,11) (18,30) (14,3) (1,29) (13,30) (26,28) (10,3) (25,17) (8,28) (17,11) (22,5) (2,16) (10,24) (0,15) (0,29) (10,4) (8,0) (23,26) (13,22) (24,20) (7,23) (13,31) (15,12) (15,19) (7,16) (27,8) (9,1) (13,0) (6,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph248",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,21) (17,23) (26,4) (17,9) (24,22) (24,7) (10,2) (15,9) (21,26) (5,12) (0,14) (12,1) (3,7) (10,27) (24,19) (20,18) (8,16) (22,13) (23,4) (23,10) (4,14) (27,12) (0,18) (11,18) (8,12) (25,0) (6,5)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph320",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,21) (4,20) (22,24) (26,10) (2,1) (16,11) (12,27) (20,0) (7,28) (23,9) (22,25) (0,22) (5,8) (5,11) (6,23) (2,25) (19,3) (23,22) (19,21) (13,22) (4,12) (15,19) (25,7) (4,19) (11,9) (17,22) (14,17) (7,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph777",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,29) (28,23) (23,21) (27,16) (11,1) (32,25) (20,32) (10,6) (15,14) (27,24) (12,2) (16,8) (17,26) (10,27) (25,18) (15,31) (22,28) (3,0) (23,5) (5,4) (2,1) (5,3) (19,7) (17,2) (14,1) (24,30) (11,10) (20,29) (32,19) (11,20) (9,13) (13,10)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph921",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (3,33) (22,25) (15,30) (0,29) (5,32) (30,32) (12,34) (5,14) (24,14) (20,27) (5,11) (12,4) (5,1) (14,29) (24,3) (0,31) (9,6) (13,22) (14,2) (2,26) (25,34) (19,24) (21,32) (23,20) (32,27) (16,28) (7,19) (8,5) (17,34) (18,24) (10,19) (2,16) (12,27) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1354",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,21) (24,9) (10,2) (2,7) (25,16) (2,11) (13,5) (8,19) (27,22) (6,19) (5,14) (27,28) (1,4) (1,19) (5,21) (0,27) (11,26) (1,0) (23,25) (15,23) (13,20) (6,26) (9,8) (27,3) (12,20) (18,1) (23,27) (25,12) (18,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1276",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (24,20) (17,5) (18,27) (2,7) (11,20) (12,14) (4,6) (4,7) (8,1) (0,19) (18,1) (23,3) (25,2) (15,22) (7,8) (21,17) (13,23) (21,23) (2,0) (0,3) (13,22) (0,1) (3,16) (14,5) (9,0) (1,22) (11,25) (26,10) (10,19) (5,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph212",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,7) (0,27) (27,24) (22,14) (26,13) (19,9) (25,10) (11,3) (25,17) (23,2) (18,9) (6,9) (14,15) (14,4) (17,1) (9,7) (26,21) (7,15) (7,16) (5,12) (1,0) (8,6) (20,24) (9,26) (10,2) (11,1) (13,12)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph909",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (25,11) (10,32) (5,17) (12,6) (11,21) (25,16) (22,12) (9,28) (32,16) (14,8) (10,7) (34,13) (1,8) (32,4) (9,11) (24,17) (25,31) (29,11) (34,30) (0,8) (23,24) (6,23) (2,33) (17,27) (30,23) (1,18) (31,15) (12,19) (2,20) (3,34) (7,6) (0,5) (23,26) (21,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph422",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (19,6) (23,1) (10,3) (1,19) (16,6) (19,7) (8,20) (27,22) (4,13) (18,6) (0,26) (4,24) (2,8) (26,28) (17,24) (2,6) (14,26) (11,29) (29,4) (11,16) (0,10) (5,16) (22,16) (25,9) (21,16) (12,8) (25,0) (24,14) (15,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph38",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,15) (2,6) (6,13) (16,5) (19,9) (8,6) (25,22) (3,21) (10,17) (15,17) (4,24) (1,11) (5,20) (19,21) (19,16) (4,12) (21,18) (23,0) (13,23) (22,13) (7,24) (23,1) (13,20) (23,7) (24,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1062",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,15) (14,7) (14,3) (17,25) (23,18) (11,12) (1,15) (0,4) (17,2) (15,25) (9,5) (24,14) (7,13) (18,10) (4,17) (22,6) (21,23) (16,10) (23,17) (1,6) (12,20) (12,6) (15,8) (14,19) (19,2) (1,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph968",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,30) (3,21) (31,27) (17,15) (2,7) (0,12) (30,26) (0,33) (11,12) (24,33) (5,11) (6,29) (34,28) (32,13) (25,23) (5,3) (29,4) (34,2) (27,28) (8,1) (9,22) (7,10) (20,28) (24,32) (14,7) (9,1) (21,16) (18,30) (19,16) (22,34) (6,21) (23,10) (15,27) (33,8)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph390",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,0) (3,10) (7,24) (19,2) (28,19) (18,19) (18,21) (21,24) (8,28) (15,27) (17,12) (7,17) (6,9) (27,17) (12,23) (14,10) (14,24) (22,1) (18,11) (24,13) (3,5) (21,22) (16,11) (25,27) (6,7) (4,26) (27,26) (7,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1455",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,9) (12,2) (1,20) (15,17) (9,3) (19,27) (6,13) (27,9) (22,3) (14,10) (0,5) (3,0) (13,9) (10,0) (0,2) (20,26) (19,2) (28,23) (4,8) (21,25) (7,15) (8,5) (25,28) (2,16) (0,4) (25,8) (1,0) (4,2) (11,8) (29,23) (23,24) (28,1) (0,15)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1217",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,14) (25,22) (11,6) (26,14) (7,27) (16,8) (9,18) (10,5) (16,19) (0,27) (25,17) (16,24) (14,3) (8,25) (9,5) (20,27) (1,27) (10,13) (6,21) (3,12) (23,14) (11,3) (0,19) (8,10) (2,19) (0,1) (0,2) (15,3) (16,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph541",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (14,11) (25,12) (8,12) (6,19) (14,4) (22,21) (21,26) (24,10) (21,13) (20,29) (2,20) (9,5) (3,1) (9,22) (30,12) (14,15) (12,7) (4,3) (22,6) (21,23) (25,13) (29,0) (2,16) (17,10) (16,10) (8,24) (26,4) (19,27) (7,28) (3,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1072",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,25) (13,21) (22,2) (6,5) (10,6) (9,19) (11,5) (5,21) (6,12) (21,24) (8,5) (0,22) (0,3) (22,18) (18,7) (4,17) (1,22) (24,16) (9,23) (1,0) (23,20) (0,14) (0,2) (14,23) (3,12) (25,20) (15,2) (4,0) (14,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph682",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,17) (16,8) (10,6) (11,1) (21,28) (23,25) (1,14) (23,19) (10,11) (4,5) (10,27) (5,3) (15,29) (1,2) (31,11) (23,29) (15,14) (0,3) (28,24) (26,20) (10,13) (13,9) (17,22) (7,19) (5,23) (11,20) (30,20) (12,2) (18,25) (16,27) (27,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph504",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,2) (27,17) (24,25) (18,9) (17,28) (29,0) (29,8) (3,28) (26,11) (28,14) (29,12) (15,7) (5,18) (20,4) (1,19) (19,21) (5,25) (21,3) (22,12) (23,3) (2,16) (5,4) (27,6) (23,10) (3,15) (11,12) (13,11) (19,26) (1,18) (29,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1697",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (22,3) (5,30) (27,24) (14,1) (12,4) (20,26) (17,31) (19,31) (20,8) (29,3) (6,11) (13,18) (26,16) (3,20) (0,2) (10,0) (21,19) (23,7) (15,27) (17,25) (23,4) (20,7) (2,17) (13,4) (1,0) (10,28) (17,15) (11,18) (28,7) (20,15) (18,30) (30,9) (14,19)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph590",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,18) (21,18) (1,10) (29,1) (8,13) (13,0) (11,25) (24,25) (21,20) (25,14) (17,30) (5,15) (26,28) (3,25) (23,24) (21,22) (19,28) (2,26) (17,9) (20,10) (16,4) (2,18) (7,17) (26,5) (1,30) (25,8) (15,16) (16,27) (18,12) (6,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph458",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,13) (3,27) (1,18) (15,0) (15,6) (29,22) (25,15) (14,8) (2,27) (2,26) (5,9) (9,17) (11,4) (16,12) (27,7) (20,22) (28,6) (21,6) (1,26) (2,10) (23,6) (20,25) (25,17) (1,12) (1,13) (5,24) (20,19) (4,14) (9,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph623",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,2) (23,9) (31,5) (14,20) (15,29) (13,22) (19,26) (6,0) (18,22) (4,13) (0,2) (23,16) (11,15) (8,15) (20,22) (21,7) (29,26) (24,14) (3,1) (5,30) (25,13) (12,7) (16,22) (26,31) (9,3) (17,21) (25,17) (14,29) (28,14) (10,1) (19,27)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph143",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,23) (24,23) (26,9) (8,4) (2,11) (2,0) (19,7) (16,7) (10,24) (5,13) (20,1) (15,1) (21,1) (17,20) (23,1) (25,8) (22,24) (3,6) (11,17) (17,16) (10,3) (9,19) (21,18) (12,16) (14,4) (13,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph689",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,14) (16,2) (1,18) (2,21) (4,18) (6,28) (16,19) (30,12) (23,14) (30,28) (27,23) (31,30) (5,14) (10,8) (21,13) (29,9) (7,8) (14,17) (7,26) (3,18) (22,8) (25,28) (27,15) (0,26) (24,10) (20,12) (22,23) (14,25) (11,28) (16,7) (4,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph535",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,2) (16,30) (15,26) (4,23) (29,3) (24,12) (28,10) (0,8) (24,19) (1,4) (3,28) (13,17) (20,23) (10,25) (28,11) (22,27) (26,9) (6,28) (17,20) (24,2) (14,3) (21,10) (8,12) (5,6) (18,8) (7,26) (29,22) (16,15) (17,22) (11,0)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph397",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,26) (11,18) (3,5) (24,13) (18,21) (27,25) (17,12) (22,21) (14,24) (28,19) (10,3) (4,26) (7,20) (7,6) (7,17) (27,15) (21,24) (19,2) (6,9) (22,1) (18,19) (12,23) (27,17) (10,14) (7,24) (16,11) (0,6) (8,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1286",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (27,17) (14,5) (2,0) (15,2) (13,8) (3,14) (18,2) (6,16) (22,16) (19,18) (1,8) (12,16) (10,15) (27,24) (11,17) (0,13) (15,12) (16,7) (3,4) (9,21) (23,8) (5,20) (24,25) (11,13) (1,0) (0,3) (9,18) (26,0) (14,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1266",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (25,4) (5,11) (19,4) (0,13) (27,7) (6,21) (6,22) (5,26) (12,5) (0,1) (24,12) (7,15) (14,18) (26,6) (7,13) (20,13) (4,16) (4,23) (8,17) (6,0) (19,9) (22,10) (14,24) (19,6) (2,23) (17,20) (3,4) (1,3)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph111",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,11) (0,21) (26,20) (4,1) (14,25) (17,25) (25,3) (10,8) (6,5) (13,21) (16,23) (13,18) (18,14) (10,16) (17,24) (17,12) (15,13) (2,5) (1,3) (17,10) (14,19) (9,25) (11,25) (14,26) (19,2) (22,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph511",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (24,12) (29,0) (25,17) (16,15) (2,30) (21,7) (28,6) (13,30) (15,25) (17,5) (10,18) (28,11) (7,14) (28,12) (28,27) (2,19) (9,8) (23,29) (12,20) (17,14) (23,18) (14,4) (4,3) (22,10) (23,6) (9,15) (26,29) (15,1) (14,19) (1,6)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph782",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,14) (27,7) (16,20) (4,15) (21,32) (23,24) (30,25) (14,21) (2,13) (4,30) (28,17) (5,20) (9,32) (8,18) (28,31) (25,6) (3,19) (11,14) (22,30) (7,29) (8,1) (18,21) (5,25) (12,9) (29,4) (17,9) (3,1) (9,23) (4,0) (2,10) (1,2) (29,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1436",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,1) (4,17) (0,1) (5,26) (10,14) (21,0) (11,2) (22,16) (12,25) (23,15) (0,28) (18,25) (20,2) (2,0) (29,20) (6,25) (8,29) (20,10) (10,5) (5,3) (27,0) (22,2) (10,13) (19,22) (28,16) (12,14) (11,15) (7,6) (10,9) (17,9) (24,11)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1693",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (5,7) (23,0) (31,20) (28,19) (17,27) (27,23) (3,9) (0,29) (14,4) (27,25) (0,3) (0,30) (13,2) (26,5) (29,6) (18,24) (23,10) (6,12) (23,18) (20,1) (26,13) (0,2) (22,4) (3,5) (8,2) (9,21) (11,28) (2,28) (16,24) (18,15) (0,1) (4,23) (4,0) (26,4) (1,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1957",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,22) (28,33) (2,3) (30,21) (2,0) (10,25) (19,11) (15,13) (5,32) (30,28) (16,25) (34,26) (8,6) (30,13) (29,9) (34,16) (4,21) (16,2) (27,20) (30,12) (1,0) (14,22) (24,18) (9,19) (19,6) (32,17) (4,31) (24,0) (20,13) (7,31) (27,22) (26,1) (6,32) (18,8) (23,8) (16,33)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1675",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,18) (0,3) (7,4) (24,9) (17,20) (22,31) (22,26) (2,22) (24,19) (26,3) (2,0) (5,7) (6,0) (25,24) (11,8) (1,14) (7,10) (21,18) (4,6) (18,12) (13,1) (27,4) (21,28) (29,10) (0,1) (16,10) (14,11) (30,17) (7,14) (18,2) (6,20) (23,19) (0,15) (20,25)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph886",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,6) (17,7) (25,8) (28,3) (17,11) (24,16) (5,31) (12,8) (32,16) (26,2) (7,21) (23,26) (33,26) (9,26) (24,15) (3,8) (33,0) (18,14) (21,13) (9,12) (27,20) (7,4) (22,1) (4,19) (10,23) (18,11) (25,20) (5,32) (9,30) (15,1) (32,30) (26,19) (13,29)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph477",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,24) (10,20) (29,12) (29,5) (24,7) (27,24) (14,12) (8,22) (22,24) (4,17) (1,15) (19,4) (6,14) (0,13) (23,28) (3,9) (21,18) (26,10) (16,8) (14,16) (9,1) (23,2) (23,11) (17,26) (19,11) (15,27) (16,0) (15,25) (6,21)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1526",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,10) (19,16) (0,16) (0,3) (5,22) (30,24) (14,13) (14,9) (28,9) (27,5) (30,25) (1,0) (1,29) (18,11) (28,7) (21,5) (0,24) (26,2) (11,5) (26,8) (23,0) (17,21) (7,12) (5,6) (20,5) (4,0) (15,16) (28,15) (27,3) (20,8) (0,2) (29,15) (18,4)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1674",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,21) (13,17) (2,10) (20,11) (22,9) (28,10) (8,7) (1,0) (20,31) (27,14) (12,13) (24,11) (25,9) (31,0) (12,19) (5,3) (5,6) (22,29) (16,3) (30,1) (28,14) (2,0) (1,29) (30,12) (15,2) (2,1) (22,24) (26,3) (18,11) (4,29) (23,5) (8,24) (19,26)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph514",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,30) (9,6) (5,24) (7,24) (24,29) (18,27) (19,5) (18,26) (15,2) (14,26) (25,20) (28,3) (8,5) (16,25) (9,12) (8,21) (1,13) (15,10) (25,1) (26,4) (6,29) (3,15) (5,22) (21,23) (26,17) (9,17) (15,13) (3,4) (4,0) (11,16)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph271",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,6) (7,1) (6,22) (4,11) (17,24) (20,13) (0,26) (21,8) (14,18) (12,20) (17,5) (8,17) (20,27) (15,11) (16,2) (15,12) (19,15) (22,15) (17,26) (17,15) (19,10) (2,19) (25,26) (18,0) (9,4) (7,23) (3,18)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph709",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,21) (4,6) (8,15) (6,8) (28,23) (4,1) (27,19) (0,12) (12,26) (7,25) (9,27) (2,1) (1,22) (19,11) (30,4) (6,11) (31,8) (13,3) (14,2) (3,1) (5,17) (32,5) (17,4) (20,15) (17,18) (23,10) (15,29) (16,26) (12,11) (16,28) (20,7) (24,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph738",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (15,0) (27,20) (13,18) (18,16) (11,14) (0,11) (30,21) (19,12) (25,8) (23,1) (7,30) (31,4) (17,10) (31,11) (32,9) (6,24) (23,28) (2,27) (22,15) (3,9) (10,16) (5,26) (29,31) (22,20) (10,2) (12,6) (7,8) (19,22) (31,5) (1,19) (32,28) (5,30)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1047",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,19) (19,15) (9,23) (7,12) (2,1) (4,19) (11,5) (4,12) (17,14) (18,21) (22,23) (20,4) (23,6) (16,11) (5,8) (0,25) (20,0) (10,22) (21,19) (24,22) (7,10) (25,2) (9,11) (22,13) (1,0) (17,22)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph970",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,27) (6,23) (3,11) (19,3) (8,18) (25,10) (27,3) (7,33) (6,17) (13,21) (14,3) (15,4) (14,30) (5,27) (7,29) (16,34) (25,32) (13,2) (5,22) (20,32) (4,28) (14,2) (26,9) (7,34) (0,20) (5,15) (2,8) (3,25) (26,18) (31,3) (12,4) (26,24) (9,1) (9,34)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph715",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,16) (13,30) (10,2) (6,13) (18,26) (28,17) (0,2) (9,12) (19,13) (22,25) (27,11) (20,9) (4,3) (4,25) (32,29) (7,20) (32,23) (19,9) (1,6) (15,20) (8,26) (18,9) (26,21) (24,4) (16,4) (24,6) (10,29) (28,12) (28,14) (22,5) (27,26) (6,31)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1592",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,22) (25,19) (2,0) (16,21) (1,27) (0,4) (16,27) (13,14) (18,6) (19,20) (0,3) (16,15) (9,4) (0,14) (11,24) (29,5) (29,10) (2,4) (17,2) (17,25) (27,8) (27,23) (5,3) (14,3) (14,12) (28,25) (14,9) (17,7) (24,18) (22,30) (5,6) (0,1) (26,25) (15,20)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1351",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,28) (21,8) (9,25) (23,27) (2,0) (2,3) (20,27) (13,27) (1,0) (21,28) (8,17) (2,13) (4,10) (12,28) (24,11) (0,5) (28,15) (20,19) (3,22) (14,28) (4,16) (10,15) (6,23) (18,25) (7,21) (5,26) (13,0) (3,4) (18,28) (10,24)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1733",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,5) (2,0) (1,7) (25,9) (31,16) (20,19) (23,24) (16,19) (0,13) (29,23) (3,11) (28,15) (6,27) (12,19) (29,1) (8,28) (24,2) (31,18) (2,9) (3,0) (4,22) (26,6) (13,7) (27,4) (17,23) (13,18) (8,11) (3,4) (6,7) (4,32) (32,30) (17,21) (22,14) (5,30) (0,1)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph282",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,18) (5,11) (26,27) (0,3) (16,0) (10,7) (21,9) (22,3) (13,11) (5,27) (6,2) (5,17) (0,24) (19,0) (2,26) (7,14) (15,23) (16,15) (1,18) (20,8) (27,24) (14,16) (4,5) (21,8) (25,15) (5,20) (12,9)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "No."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1713",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,10) (26,18) (16,8) (4,15) (17,1) (17,31) (25,28) (2,7) (0,15) (6,30) (9,23) (0,27) (1,0) (19,11) (7,26) (31,26) (28,10) (0,2) (2,22) (14,17) (21,0) (32,3) (5,3) (4,10) (24,23) (26,12) (13,2) (30,31) (24,2) (28,20) (11,22) (30,10) (24,32) (0,3) (29,14)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    },
    {
        "id": "cycle-hard-graph1460",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (29,12) (19,3) (15,14) (4,16) (21,26) (16,6) (15,11) (29,25) (25,20) (4,24) (17,12) (7,28) (27,6) (8,1) (24,3) (0,27) (26,29) (28,18) (16,8) (15,23) (19,25) (5,24) (11,18) (9,22) (13,10) (9,4) (1,13) (2,12) (9,28)<\nIs there a cycle in this undirected graph?"
            },
            {
                "from": "gpt",
                "value": "Yes."
            }
        ]
    }
]